A MIXED ANALOG AND DIGITAL PIXEL ARRAY

DETECTOR

FOR SYNCHROTRON X-RAY IMAGING

A Dissertation

Presented to the Faculty of the Graduate School

of Cornell University

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

by

Daniel R. Schuette

August 2008

This document is in the public domain.

A MIXED ANALOG AND DIGITAL PIXEL ARRAY DETECTOR

FOR SYNCHROTRON X-RAY IMAGING

Daniel R. Schuette, Ph.D.

Cornell University 2008

We present description and documentation of the development and first applica-

tions of the Mixed–Mode Pixel Array Detector, a new type of imaging detector

for synchrotron based x-ray science. Today there exists a great gulf between the

intense x-ray fluxes that modern synchrotron light sources are capable of produc-

ing and the capabilities of imaging detectors to measure the resulting signal. This

detector is intended to help bridge this gulf by offering readout times of less than

1 ms, a dynamic range extending from single x-rays to a full well of more than

2.6× 107 x-rays/pixel, capable of measuring fluxes up to 108 x-rays/pixel/s, with

a sub-pixel point spread. These characteristics exceed, by orders of magnitude,

the capabilities of the current generation of x-ray imagers. As a consequence this

imager is poised to enable a broad range of synchrotron x-ray experiments that

were previously not possible.

BIOGRAPHICAL SKETCH

Daniel R. Schuette was born in Iowa in 1977. He attended Washington High

School in Cedar Rapids, Iowa from 1992 to 1996. As an undergraduate he attended

the University of Chicago from 1996 to 2000, graduating with honors degrees in

Mathematics (B.S.) and Physics (B.A.). From 2000 to 2001 he worked as a re-

search associate on the Solar Tower Atmospheric Cherenkov Effect Experiment

(S.T.A.C.E.E.); first at the University of Chicago’s Enrico Fermi Institute then

with the Department of Physics and Astronomy at the University of California,

Los Angeles. Following this, in the fall of 2001, he entered graduate studies at

Cornell University, receiving his M.S. in Physics in January of 2005 and then his

Ph.D. in Physics in August of 2008.

v

In memory of Raphael H. Kapfer (1977–2002)

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ACKNOWLEDGEMENTS

A thesis in experimental physics is built on the work of many people; some

directly involved in the work of the project, some who facilitate this work by pro-

viding material support or direction, and some who provide the ideas that the work

is built upon. This is evident even in a relatively small project like the Mixed–

Mode Pixel Array Detector (PAD). In this project the combined efforts of a large

group of people, involved in different aspects of the project’s planning and man-

agement as well as the detector design, fabrication, packaging, and testing, were

required to bring about a functioning detector along with the array of supporting

electronics, hardware, and software needed to make it functional. Beyond those

who worked directly on the Mixed–Mode PAD there are also many people who

deserve my thanks for their help in preparing me for this undertaking and aiding

me throughout it. I consider myself fortunate to have been in an environment

at Cornell that fostered developing the skills needed for this task by providing a

wonderful group of mentors and compatriots. Because of either their direct contri-

butions to developing the Mixed–Mode PAD or their indirect assistance, through

the guidance and education they offered me, many people deserve my thanks. My

apologies to anyone who might have been left off this list.

First and foremost I must thank my thesis advisor, Sol Gruner, for making this

entire undertaking possible. Sol has been my advisor since the day I arrived at

Cornell, nearly seven years ago. During this time there have been many successes,

a few failures, some hard times, and some great ones. Throughout it all Sol has

been invaluable, with his support, direction, patience, and understanding.

My other committee members, Jim Alexander, Alyssa Apsel, and Brad Minch

also deserve thanks for watching over my progress at Cornell. In particular I would

like to thank Brad, who was willing to devote a significant amount of time in the

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early days of my studies at Cornell teaching me the basics of low-noise Mixed-

Analog-Digital VLSI design.

Cornell is fortunate to have a small but vibrant detector x-ray development

group, which I have been a member of for most of my Ph.D. tour. Thanks to

the other members of the Cornell X-Ray Detector Development Group, past and

present: Mark Tate, Matt Renzi, Alper Ercan, Lucas Koerner, Hugh Philipp, Mar-

ianne Hromalik, and Darol Chamberlain. To these people, I am greatly indebted

for their many exchanges of ideas and equipment over the course of this thesis, as

well as support in preparation and execution of the PAD CHESS runs. Within

this group Mark, Matt, and Lucas deserve special recognition. Mark, for the ex-

perience, advice, and assistance that he brings to detector development and his

willingness to pass these on to inexperienced graduate students. Matt, who was

the senior graduate student when I started working on PADs and who supervised

me in my first year. And last, but definitely not least, Lucas whose help has been

invaluable in the most recent years of this project, particularly in preparing for

and carrying out runs at CHESS.

Thanks also goes out to our collaborators at Area Detector Systems Corpo-

ration (ADSC). This group handled most of the packaging issues related to the

hybrids as well as working in concert with Cornell on the detector design and

testing. specifically Ron Hamlin, Tom Hontz, Wayne Vernon, Matt Allin, Skip

Augustine, Don Abbe, and Doan Nyugen with whom I have worked closely over

the duration of this project.

Returning to Cornell, I am indebted to the many people who have passed

through the Gruner lab during my stay here. Most prominent in this group were

Gil Toombes and Thalia Mills who, beyond being good friends and admirable

scientists, often helped me with my children; watching over them when I had to

x

attend meetings or accomplish work at the lab. In addition to Gil and Thalia, there

are many people whom I have benefitted from knowing and working with: Pascale

Chenevier, Anurag Jain, Raphael Kapfer, Marcus Collins, Nozomi Ando, Chae Un

Kim, Yi-fan Chen, Darren Southworth (who briefly worked on the Mixed–Mode

PAD), Dag Anderson, Tom Caswell, and Buz Barstow to offer an extensive, but

not all inclusive, list. Finally, in the Gruner lab, our machinist, Marty Novak,

deserves special thanks for the wonderful camera housings that he built.

Then, thanks to all the people who have kindly read through and helped me

copy edit this thesis; in particular Kate Green, who reviewed this work from cover

to cover.

I also wish to thank the various sponsors throughout my graduate career that

made this work possible: Cornell University for a G-line fellowship and the U.S.

Department of Energy for support of detector work by our Cornell Group (grants

DE-FG02-97ER62443, and DE-FG02-97ER14805). The primary support of this

work was a subcontract from ADSC’s National Institute of Health grant RR014613

(Dr. Ron Hamlin, P.I.). Part of this work was performed at the Cornell High

Energy Synchrotron Source (CHESS), which is a national user facility supported

by the National Science Foundation and the NIH/NIGMS under Award DMR-

0225180.

Although only indirectly related to my dissertation work, Corbin Covault de-

serves my thanks for introducing me to research in physics while I was an under-

graduate at the University of Chicago. I also owe a great debt of thanks to Rene

Ong, my undergraduate advisor at the University of Chicago, for his mentoring,

when I was an undergraduate, and friendship, in those years and the years since.

Finally, thanks to my family. To my parents, who were my first teachers. To

my wife Dorothy—without all her love, patience, and support (not to mention

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editing skills) this thesis would not have been possible. To my elder son, Henri,

who made sure I set the thesis aside and went out to play now and then. And to

my younger son, Conall, who has been my consistent companion through much of

this writing and a persistent reminder of how long this task has taken to complete.

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TABLE OF CONTENTS

Biographical Sketch v

Dedication vii

Acknowledgements ix

Table of Contents xiii

List of Figures xvii

List of Tables xxxi

List of Abbrevations xxxiii

List of Symbols xxxv

1 Introduction 11.1 X-Rays & Synchrotron Light Sources . . . . . . . . . . . . . . . . . 21.2 Need for New Detectors . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Document Organization . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Pixel Array Detector Fundamentals 92.1 PAD Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 PAD Semiconductor Physics . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Charge Concentration . . . . . . . . . . . . . . . . . . . . . 162.2.2 Charge Transport . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.2.1 Generation and Recombination . . . . . . . . . . . 182.2.2.2 Pure Diffusion . . . . . . . . . . . . . . . . . . . . 192.2.2.3 Diffusion within a Constant Electric Field . . . . . 192.2.2.4 Diffusion in a Linear Electric Field . . . . . . . . . 21

2.2.3 Basic Semiconductor Devices . . . . . . . . . . . . . . . . . 222.2.3.1 P/N Junction Diode . . . . . . . . . . . . . . . . . 222.2.3.2 The MOS Capacitor . . . . . . . . . . . . . . . . . 25

2.3 Radiation Effects in Silicon . . . . . . . . . . . . . . . . . . . . . . . 282.3.1 X-Ray Detection in the Mixed–Mode PAD . . . . . . . . . . 312.3.2 Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.2.1 Single Event Effects . . . . . . . . . . . . . . . . . 352.3.2.2 Long-Term Damage . . . . . . . . . . . . . . . . . 37

3 Mixed–Mode PAD Prehistory 493.1 Digital Pixel Array Detectors . . . . . . . . . . . . . . . . . . . . . 503.2 Analog Pixel Array Detectors . . . . . . . . . . . . . . . . . . . . . 533.3 Contemporary PAD Projects . . . . . . . . . . . . . . . . . . . . . . 56

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3.4 Mixed–Mode Pixel Array Detector . . . . . . . . . . . . . . . . . . 58

4 Mixed–Mode PAD Pixel Design 614.1 Mixed–Mode PAD Pixel Architecture . . . . . . . . . . . . . . . . . 634.2 Primary Pixel Components . . . . . . . . . . . . . . . . . . . . . . . 67

4.2.1 Pixel Integrator . . . . . . . . . . . . . . . . . . . . . . . . . 684.2.1.1 Integrator Amplifier – Performance Specifications . 704.2.1.2 Integrator Amplifier – Architecture and Analytical

Analysis . . . . . . . . . . . . . . . . . . . . . . . . 704.2.1.3 Integrator Amplifier – Performance Characteristics 784.2.1.4 Integrator Amplifier – Noise Performance . . . . . 834.2.1.5 Radiation Tolerance . . . . . . . . . . . . . . . . . 924.2.1.6 Integrator Linearity . . . . . . . . . . . . . . . . . 96

4.2.2 Quantized Charge Removal . . . . . . . . . . . . . . . . . . 974.2.2.1 Analog Components: The Gory Details . . . . . . . 984.2.2.2 A Question of Fidelity: The Pixel Virtual Ground . 1014.2.2.3 Charge Removal Controller . . . . . . . . . . . . . 1084.2.2.4 Charge Removal Conclusions . . . . . . . . . . . . 111

4.2.3 In-pixel Counter . . . . . . . . . . . . . . . . . . . . . . . . 1134.2.3.1 Pseudorandom Counter . . . . . . . . . . . . . . . 1134.2.3.2 Linear Alternatives . . . . . . . . . . . . . . . . . . 1144.2.3.3 Counter Conclusions . . . . . . . . . . . . . . . . . 115

4.3 Periphery Pixel Components . . . . . . . . . . . . . . . . . . . . . . 1164.3.1 Pixel Diagnostic Circuit . . . . . . . . . . . . . . . . . . . . 117

4.3.1.1 Control Shift Register . . . . . . . . . . . . . . . . 1174.3.1.2 Analog MUX and Output Buffer . . . . . . . . . . 1204.3.1.3 Test Current Source . . . . . . . . . . . . . . . . . 123

4.3.2 Mixed-Mode PAD CDS . . . . . . . . . . . . . . . . . . . . . 1234.3.2.1 General CDS . . . . . . . . . . . . . . . . . . . . . 1254.3.2.2 CDS Transfer Function . . . . . . . . . . . . . . . . 1264.3.2.3 Effect of CDS on Low-Pass-Filtered White Noise

Source . . . . . . . . . . . . . . . . . . . . . . . . . 1274.3.2.4 Noise Comparison without CDS . . . . . . . . . . . 1274.3.2.5 Analog CDS Fidelity . . . . . . . . . . . . . . . . . 1314.3.2.6 Conclusions on the Mixed–Mode PAD Analog CDS 132

4.3.3 Pixel Sample and Hold . . . . . . . . . . . . . . . . . . . . . 1334.3.3.1 Digital CDS . . . . . . . . . . . . . . . . . . . . . . 135

4.4 Design Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5 Single Hybrid Camera 1395.1 System Breakdown and Decomposition . . . . . . . . . . . . . . . . 139

5.1.1 Camera Housing and Detector Cryostat . . . . . . . . . . . . 1415.1.2 High-Speed, Low-Noise Support Electronics . . . . . . . . . 1425.1.3 Data Acquisition and Control . . . . . . . . . . . . . . . . . 144

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5.1.3.1 Control Clock Pattern Generation . . . . . . . . . 1475.1.3.2 Readout and Frame Buffering . . . . . . . . . . . . 148

5.2 Selected Control Clock Patterns . . . . . . . . . . . . . . . . . . . . 1505.2.1 Bias/Reference DACs & Global Control Register . . . . . . 1525.2.2 Pixel Exposure Control . . . . . . . . . . . . . . . . . . . . . 1525.2.3 Pixel Control Shift Register . . . . . . . . . . . . . . . . . . 1535.2.4 Pixel Readout Control . . . . . . . . . . . . . . . . . . . . . 154

5.2.4.1 Digital Readout Clock Timing . . . . . . . . . . . . 1555.2.4.2 Analog Readout Clock Timing . . . . . . . . . . . 1565.2.4.3 CKD & CKA Interweaving . . . . . . . . . . . . . 156

6 Detector Characterization 1596.1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1606.2 Pixel Electronic Noise . . . . . . . . . . . . . . . . . . . . . . . . . 1686.3 Charge Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1726.4 Spatial Response and Resolution . . . . . . . . . . . . . . . . . . . 177

6.4.1 Discrete Sampling of Limited Active Area . . . . . . . . . . 1786.4.2 Data Collection and Refinement . . . . . . . . . . . . . . . . 1806.4.3 Spatial Characterization Measurements . . . . . . . . . . . . 182

6.4.3.1 Spatial Response Curves . . . . . . . . . . . . . . . 1856.4.3.2 Modulation Transfer Function . . . . . . . . . . . . 1946.4.3.3 Contrast Transfer Function . . . . . . . . . . . . . 195

6.4.4 Spatial Response Inhomogeneity . . . . . . . . . . . . . . . . 1976.5 Detector Quantum Efficiency . . . . . . . . . . . . . . . . . . . . . 2036.6 Detector Calibrations and Corrections . . . . . . . . . . . . . . . . 207

6.6.1 Analog and Digital Data Combination. . . . . . . . . . . . . 2096.6.2 Pedestal Offset . . . . . . . . . . . . . . . . . . . . . . . . . 2116.6.3 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . . . . . 2126.6.4 Distortion Correction . . . . . . . . . . . . . . . . . . . . . . 214

6.6.4.1 Image Correction Transforms . . . . . . . . . . . . 2156.7 Radiation Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . 221

6.7.1 Comments on Units and Dose . . . . . . . . . . . . . . . . . 2226.7.2 Bare ASIC Damage . . . . . . . . . . . . . . . . . . . . . . . 2256.7.3 Hybridized ASIC Damage . . . . . . . . . . . . . . . . . . . 2326.7.4 Conclusions on Radiation Tolerance . . . . . . . . . . . . . . 236

6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

7 First Mixed–Mode PAD Experiments 2397.1 Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2397.2 Wide Angle Scattering From Sheet Aluminum . . . . . . . . . . . . 2467.3 Fine-sampled Image Resolution . . . . . . . . . . . . . . . . . . . . 2497.4 Protein Crystallography . . . . . . . . . . . . . . . . . . . . . . . . 254

7.4.1 Overview of Protein Crystallography . . . . . . . . . . . . . 2547.4.2 Data Collection–Towards Finely Slicing the φ . . . . . . . . 258

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7.4.3 Synchrotron Measurements . . . . . . . . . . . . . . . . . . . 2627.4.3.1 CHESS F2 Beamline . . . . . . . . . . . . . . . . . 2637.4.3.2 Full-Sized Detector Mosaic Diffraction Image . . . 2637.4.3.3 Spot Comparison . . . . . . . . . . . . . . . . . . . 2637.4.3.4 Continuous Crystal Rotation: φ-Profiling . . . . . . 264

7.4.4 Reflections on Protein Crystallography . . . . . . . . . . . . 2697.5 Time-Evolving Systems . . . . . . . . . . . . . . . . . . . . . . . . . 271

7.5.1 PLD Overview . . . . . . . . . . . . . . . . . . . . . . . . . 2737.5.2 PLD Studies by the Brock Group at CHESS . . . . . . . . . 2747.5.3 Synchrotron Studies of Monolayer Growth . . . . . . . . . . 277

7.5.3.1 CHESS G3 Beamline . . . . . . . . . . . . . . . . . 2777.5.3.2 Homoepitaxial SrTiO3 Growth . . . . . . . . . . . 278

7.5.4 Mixed–Mode PAD Performance Critique . . . . . . . . . . . 2847.5.5 Prospects for 2D Growth . . . . . . . . . . . . . . . . . . . . 286

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

8 Conclusions 2898.0.1 Performance Highlights . . . . . . . . . . . . . . . . . . . . . 2908.0.2 Science Opportunities . . . . . . . . . . . . . . . . . . . . . 2928.0.3 Work Ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . 2938.0.4 Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . 294

A Linear Feedback Shift Register Theory 295

B Frequency Analysis of Integrator with Injected Current 299

C ASIC Submission History 301

Bibliography 303

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LIST OF FIGURES

2.1 Artist’s conception of a Pixel Array Detector (PAD) illustrating:the detector diode layer, responsible for converting photons intoelectrical charge; the signal processing application specific inte-grated circuit (ASIC) layer, responsible for processing the signalgenerated by the detector diode; and the array of bump bonds thatprovide electrical interconnects between corresponding pixels on thediode layer and the ASIC. Thanks to Hugh Philipp for the image. . 10

2.2 Comparison of the indirect method of x-ray detection used in phos-phor coupled CCDs with the direct detection approach of PADs.Panel (a) offers a cut away of a CCD detector showing: the phos-phor screen, that converts x-rays into optical light; the optical ta-per, that collects and transits this light; and the CCD which quan-titatively records the light. Panel (b) describes the detector diodelayer of a PAD hybrid, illustrating: the uniform n+ region at thediode surface, used to distribute the reverse bias voltage; the n−region in the detector bulk, where x-rays directly convert into pho-tocurrent; and the pixelated p+ regions at the base of the detectorwhere the photocurrent is collected. Neither figure is drawn to scale. 11

2.3 Energy band diagram of a reverse biased P/N junction. . . . . . . 232.4 Semiconductor band diagrams depicting the accumulation, flat band,

depletion, and inversion states of a p-type substrate. The parame-ter ψs represents the surface potential induced by the applied voltage. 26

2.5 Absorption properties of silicon. Panel (a) shows absorption lengthas a function of energy. Panel (b) show the relative absorptionefficiency of a 500 μm detector diode layer to normally incident x-rays. Values for these plots were obtained from the Berkeley Lab,Center for X-Ray Optics web site (www.cxro.lbl.gov), which in turncites [46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.6 Model used for calculating the charge yield profiles of a monochro-matic x-ray beam incident on a fully depleted silicon diode. They = 0 plane is defined by the vertical plane containing path of thex-ray, while the the x = 0 plane is defined to be the vertical planeperpendicular to the y = 0 plane, containing the point where thex-ray enters the diode. . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.7 Charge yield profiles of monochromatic x-ray beams of differingenergies at incidence angles of 0, 5, 10, 15, and 20 deg. from thesurface normal of a 500 μm detector diode. The cutoffs exhibited inthe 12 keV and 16 keV plots, panels (c) and (d), at high incidenceangles are due to x-rays passing completely through the 500 μmthick diode layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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2.8 Illustration of a sub-μm CMOS layout (shallow trench isolation) in-dicating regions susceptible to radiation damage. Panel (a) depictsa transistor cross section taken along the dashed line indicated bythe star encircled ‘a’ in panel (b), which, in turn, depicts the topview of a transistor layout. In both panels, region 1 denotes whereionization induces transistor threshold voltage shifts, region 2 de-notes where ionization induces the formation of parasitic transistorsbetween the source and drain diffusions of a nMOS device, and re-gion 3 denotes where ionization induces the formation of parasitictransistors in the field oxide. . . . . . . . . . . . . . . . . . . . . . 38

2.9 Illustration of an Enclosed Layout Transistor (ELT) in contrast tothe traditional linear transistor. . . . . . . . . . . . . . . . . . . . . 42

2.10 Three amplifier architectures offering similar performance charac-teristics but drastically different levels of radiation tolerance. Am-plifiers are ordered from left to right in order of increasing radiationtolerance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1 High level description of the Mixed-Mode PAD pixel architecture. . 644.2 Voltage traces acquired from active nodes within the pixel (AE176

submission), labeled as in figure 4.1, illustrating operation with aconstant test current source. . . . . . . . . . . . . . . . . . . . . . 65

4.3 Schematic of the pixel integrator. . . . . . . . . . . . . . . . . . . . 684.4 Schematic of Mixed–Mode PAD integrator amplifier. Transistor

sizing and multiplicity are given in table 4.2. The bulk of transis-tors M1 and M2 are connected to their common source. All otherbulks are connected to the analog supply (VDDA) or analog ground(VGNDA) as is appropriate by type. No stabilization capacitor isneeded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.5 Model circuit used to analyze the effective transconductance of thenMOS folded cascode. . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.6 Mixed–Mode PAD integrator amplifier transconductance as a func-tion of differential mode input voltage. . . . . . . . . . . . . . . . . 80

4.7 DC sweep simulation of the Mixed–Mode PAD integrator amplifier.A line of unity slope through the origin is included for reference. . 81

4.8 Bode plot depicting the frequency response of the Mixed–ModePAD integrator amplifier under its nominal, 5 μA bias, operatingconditions. This figure shows that the unity gain bandwidth of theamplifier is ∼30 MHz with a phase margin of nearly 45 deg.. . . . . 82

4.9 Simulated noise power spectra for the Mixed–Mode PAD integra-tor amplifier. The first plot shows the differential Noise SpectralDensity (NSD) while the second shows the integrated Noise Spec-tral Density (NSD) as a function of the sample & hold bandwidth,assuming a 100 second integration time. . . . . . . . . . . . . . . . 84

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4.10 Power Supply Rejection Ratio (PSRR) of Mixed–Mode PAD in-tegrator amplifier in unity gain feedback configuration, i.e. resetswitch closed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.11 PSRR of Mixed–Mode PAD integrator amplifier in capacitive feed-back configuration, i.e. reset switch open. . . . . . . . . . . . . . . 87

4.12 Model system for analyzing the effect of capacitive coupling be-tween VDDA and the inverting input of the amplifier. . . . . . . . . 88

4.13 Simulated CMRR for Mixed–Mode PAD integrator amplifier. . . . 914.14 Panel (a) shows a simulation of the change in the integrator out-

put over time in response to a constant signal current allow with adashed line showing the ideal response. Panel (b) shows the devi-ation of the simulated response from the ideal response. . . . . . . 96

4.15 Schematic of the switched capacitor quantized charge removal cir-cuit found in the analog front end of each pixel. This circuit per-forms the Δ-portion of the ΣΔ-operation discussed in section 4.1. . 98

4.16 Analog input model used to derive the current transfer function,H(ω). This model lumps the capacitance of the charge removalcapacitor (Crem) into the parasitic front end capacitance (Cpar). . . 102

4.17 Examples of the current transfer function (the integrand of equation4.45) for the Mixed–Mode PAD integrator amplifier at four differentτrem values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.18 Fraction of charge accumulated onto the charge removal capacitor,for a pixel operating in the linear range, during a charge removaloperation of duration trem = 2τrem using the Mixed–Mode PADintegrator amplifier. In most cases a few additional considerationsare required because the quantity of charge removed will, temporar-ily, take the pixel out of the range of linear approximation. Theseconsiderations are outlined at the end of section 4.2.2.2. . . . . . . 107

4.19 Schematic of the charge removal control circuit. . . . . . . . . . . . 1094.20 General architecture of the linear feedback shift register based pseu-

dorandom counter. Figure adapted from [47]. . . . . . . . . . . . . 1144.21 Elements of the pixel diagnostic circuit. Panel (a) shows the shift

register used to control the diagnostic circuit (i.e. the Control ShiftRegister or CSR). Panel (b) shows the analog MUX and outputbuffer used to drive waveforms within the pixel to test point on theASIC periphery. Panel (c) shows the test current source connectedto the integration node of each pixel. . . . . . . . . . . . . . . . . . 116

4.22 Small-area single-phase shift register element. . . . . . . . . . . . . 1194.23 Performance characteristics of the diagnostic buffer amplifier. . . . 1214.24 Schematic of the Mixed-Mode PAD CDS implementation. . . . . . 1244.25 Post CDS-filtering of low-pass-filtered white noise spectra for dif-

ferent combinations of τn and Δts. These figures illustrate howstrongly the effectiveness of CDS is influenced by the ratio of thethese two time constants. . . . . . . . . . . . . . . . . . . . . . . . 128

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4.26 Normalized total output noise (NCDS) of a low pass filtered whitenoise spectrum with noise power An and filter constant τn afterCDS with sampling time Δts. . . . . . . . . . . . . . . . . . . . . . 129

4.27 Schematic description of the pixel sample and hold circuit. . . . . . 1344.28 Performance characteristics of the sample and hold isolation buffer. 135

5.1 Photograph of the cryostat housing the Mixed–Mode PAD singlehybrid camera along with the FPGA control and frame buffer usedin the camera. Not shown is the electronics rack containing thedata acquisition control computer. . . . . . . . . . . . . . . . . . . 140

5.2 Photographs of the Mixed–Mode PAD from different perspectives.The plastic tubing snaking from the top of the back plate carrychilled water, left and center tube in panel (a); and supply thevaccuum connection, right tube in panel (a). Panel (c) exposes thethermelectric-cooled cold finger. . . . . . . . . . . . . . . . . . . . . 141

5.3 Control and data flow within the Mixed–Mode PAD Single HybridPrototype data acquisition & control system. . . . . . . . . . . . . 145

5.4 Relation between the Mixed–Mode PAD digital control signals, asdefined in table 5.1, and systems on the detector hybrid. TheCKEN signal does not directly affect any system on the chip, butis intended to act as a gate for the various system clocks to preventerrant cycles. On the AE207 submission, however, there is an errorin the implementation of this line, and, thus, its use is not advised. 150

5.5 Timing for programming the on-chip bias and reference generating6-bit DACs as well as the global control register. Data is latched onthe falling edge of the DACCK signal so that the waveform shownhere would load a hypothetical sequence of 01010 . . . 1. . . . . . . . 151

5.6 Timing diagram for the control of an exposure in the cases whereanalog CDS is used, panel (a), and where it is not, panel (b). Notethat the location of tbgn changes between these two cases. . . . . . 153

5.7 Timing for programming the pixel control shift register. The datashown represents a hypothetical sequence of 101 . . . 01. . . . . . . . 154

5.8 Timing controlling the readout of the Mixed–Mode PAD digitaldata. MRST and CKD are external signals defined in table 5.1while the DLATCH and DIGADV signals are derived signals gen-erated internally on each hybrid. The DLATCH signal causes thedigital data on the array bus to be latched into the output shiftregister while DIGADV shifts data from the in pixel data registeronto digital data bus of the array. . . . . . . . . . . . . . . . . . . . 156

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5.9 Timing controlling the readout of the Mixed–Mode PAD analogdata as well as the row select logic for the digital data. MRSTand CKD are external signals defined in table 5.1 the ROWSELsignal is a derived signal generated internally on each hybrid. TheROWSEL signal is responsible for advancing the row select shiftregister (a 128 element single-shot shift register, reset when MRSTis asserted). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.10 Combined readout clock sequencing used in the single hybrid cam-era. In this diagram, the CKD signal is not shown at full resolutiondue to space limitations. Instead, in its first active region, thereare two cycles, and, in each subsequent region, there are sixteen cy-cles (denoted by the high/low logic region). The ANAREC signaldenotes the sampling clock used by the ADCs to time recording ofthe analog data. Because of the internal structure of the ADCs itmust be periodic, resulting in two redundant samples for every 16pixels worth of analog data. The first valid digital data comes offthe chip in period 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.1 Linearity of the digital portion of the Mixed–Mode PAD data stream,shown as the rate of charge removals as a function of stimulatingcurrent. This measurement was made by sourcing a known currentonto the pixel integration node via a needle probe connection to anunbonded pixel, in the manner discussed within the text. . . . . . . 161

6.2 Average per-pixel leakage current from observed by interior pixelsof a Mixed–Mode PAD hybrid as a function of temperature. Thedependent axis is plotted in terms of mV/pixel/second, becausethis is what is directly measured from the integrator. The directconversion to charge depends on the absolute conversion factor ofthe integrator in each pixel, which, in turn, depends on the size ofthe integration capacitor. The integration capacitor was laid outhave a capacitance of 50 fF, however, measurements indicate thatits actual capacitance is 20% to 30% larger than expected. . . . . . 162

6.3 Traces from a pixel integrator output under the stimulus of thediode leakage current. Panel (a) was taken with Vref , Vlow, and Vth

set to extend the range of Voutp into the nonlinear region of theintegrator. In panel (b), Vref , Vlow, and Vth were set to show thelinear range of the integrator. Under normal operating conditionsVref , Vlow, and Vth are set so that the integrator output will remainwithin a ∼ 1 V subset of this range. In both panels a linear fit isshown to illustrate the integrator linearity or deviance therefrom. . 164

6.4 Typical analog (Voutp), digital (NΔQ), and merged (Veqv) data forone pixel from leakage current integration series. Detector was heldat 20 deg. C, isolated from ambient light during these exposures. . 165

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6.5 Typical merged analog and digital data (Veqv) from one pixel in a Cux-ray tube exposure series. For this series, the tube was operatedat 25 kV with a current of 0.4 mA, hybrid temperature was set at20 deg. C. Data scaling factors were calculated from dark currentintegration series as discussed in the text. . . . . . . . . . . . . . . 167

6.6 Two pixel RMS distributions derived from the same series of 25frames taken where all frames had the same integration time. TheGaussian peaked at a right, larger average RMS, was derived fromuncorrected data while the Gaussian at the left, smaller averageRMS, was corrected for global shifts in the array via a mean sub-traction. This data assumes a 1 mV = 1 keV conversion gain. . . . 169

6.7 Detector noise as a function of accumulated diode leakage currentwith the hybrid maintained at +20 deg. C in the camera. To gener-ate this figure, measurement statistics were calculated from sets of25 images acquired at 1000 integration times randomly distributedfrom 1 ms to 1 s. The range of signal observed was divided into75 evenly spaced bins into which the mean per-pixel RMS values,based on a Gaussian fit as described in the text, were divided basedon their corresponding mean signal. The data point plotted thenindicates the mean, mean per-pixel RMS in each bin and the errorbars indicate the RMS fluctuations about this mean. The unitson the horizontal and vertical axes are given in equivalent 10 keVx-rays (assuming a 1 mV = 1 keV conversion gain) to make the com-parison to an experimental signal more straightforward, althoughthe ordinate axis could equivalently have been labeled in time span-ning up to 1 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6.8 Detector noise observed over a series of diode leakage current inte-gration extending from 1 ms to 100 s, taken with and without CDS.For these measerements the hybrid was maintained in the camerahousing at -25 deg. C and exhibited an average leakage level 29.5x-rays/s (assuming a 1 mV = 1 keV conversion gain). . . . . . . . 171

6.9 Multipixel x-ray spot generated by a Cu target rotating anodesource, imaged at differing detector diode reverse bias voltages. Im-ages were acquired with identical integration times and are shadedusing the same logarithmic grey scale, to bring out both faint andintense features. Vertical and horizonal axis units are mm. . . . . . 173

6.10 From selected images in figure 6.9, x-ray spot intensity profile takenalong a vertical line through the center of the pixel, for differingdetector diode reverse bias voltages. . . . . . . . . . . . . . . . . . 174

6.11 Total acquired dose, integrated across the full detector, of a floodfield as a function of detector diode bias. The flood field was gen-erated by a Cu x-ray tube biased at 25 kV and the integration timewas held constant over all measurements. Results are normalizedto the dose measured at a bias of VHV = 150 V. . . . . . . . . . . . 175

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6.12 Mixed–Mode PAD charge collection. These figures show the chargecollection from a 75 μm spot source of x-rays as it is translated alonga line near the bisector of three pixels sharing the same row. Panels(a), (b), and (c) show the dose collected in each pixel normalizedagainst the average of the sum of the dose measured in the threepixels at each spot location. These individual measurements arecombined in panel (d) along with the sum of the dose measured inthe three pixels at each spot location (denoted by the open circleswith error bars). This measurement indicates that no charge is lostin the regions between pixels. . . . . . . . . . . . . . . . . . . . . . 176

6.13 Parallax model used for the derivation of equations 6.17, 6.18, and6.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

6.14 Spot pattern images taken with the Mixed-Mode PAD when illumi-nated with an x-ray flood field occulted by pin-hole mask. In theseimages, the holes on the 50 μm thick Tungsten mask are 75 μm indiameter arranged in a grid with 1 mm × 1 mm spacing. Panels(a) and (b) depict a single image while panels (c) and (d) representa filtered combination of many images in which the detector wastranslated in sub-pixel steps relative to the pattern of spots. . . . . 187

6.15 Pixel Spot Response (PSR) to illumination with a flood field oc-culted by a 75 μm circular aperture. The ordinate axis of bothpanels (a) and (b) are along the imager’s row/column axes. Sliceprofiles taken horizontally (c), diagonally (d), and vertically (e)through the 2D response function illustrate the symmetries of thesystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.16 Discrete deconvolution of the pixel spot response. Panel (a) showsa deconvolution initiated at the left and carried out over the wholedata set. The increasing fluctuations in the resulting deconvolutionare due to noise amplification effects that result from the recursiveform of the algorithm. Panel (b) shows the result of two half decon-volutions initiated from either side of the data set. This methodgives an accurate representation of the extent of the pixel pointsource response; however, it still suffers from error amplificationin its interior region. In both panels, a dashed line is included toindicate the pixel spot response. . . . . . . . . . . . . . . . . . . . 190

6.17 Comparison of the measured diagonal pixel spot response profile(dashed line) with the form calculated under the assumption ofseparability from the vertical and horizontal response profiles (dots).191

6.18 Linear averaged pixel response curves. The ordinate axis of bothpanels (a) and (b) are along the row/column axes and assume thatthe knife edge of the occultation mask is perpendicular to this axis. 192

6.19 Modulation Transfer Function (MTF) calculated from the imagerLSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

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6.20 Real space Contrast Transfer Function (CTF) response at particu-lar spatial frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.21 Comparison of the Mixed–Mode PAD Modulation Transfer Func-tion (MTF), discrete Contrast Transfer Function (CTF) measure-ments, and the Nyquist Limit imposed by the imager sampling grid. 197

6.22 Background subtracted and mean intensity normalized flat field re-sponse from Cu and Mo x-ray tube sources (25 keV and 30 keVtube bias resp.) as measured with the same Mixed–Mode PADhybrid biased at 150 V. Both images are shown on a gray scalespanning ±10% of the mean intensity. A ∼1 m collimator sepa-rated the imager from the x-ray source. In addition, a 794 μm Alattenuator was used to suppress the bremsstrahlung component ofthe Mo spectra with the main effects evident below 10 keV. . . . . 198

6.23 Calculated profile of the drift time (tdrift) for holes, in a 500 μmdiode biased at 150 V, generated by normally incident x-ray beamsof 8.05 keV, 13.0 keV, and 17.5 keV, based on equations 2.19 and2.30. The dotted vertical lines denote the mean drift time for thecurve denoted by their end points (38 ns, 48 ns, and 84 ns resp.). . 200

6.24 Intensity profile drawn across the same line on the same hybridshowing the variation in distortion with detector diode bias, nor-malized to the mean intensity at a bias of 150 V. The line shownhere was chosen to be roughly normal to the arcs of intensity dis-tortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

6.25 Detector Quantum Efficiency normalized to Quantum Efficiency ofthe detector. The error bars included with the data indicate the dis-tribution of RMS computed from the individual illumination spots.Due to systematic variation between the different spots this RMSis much larger than the fluctuation between DQE/QE2 measure-ments, as evident by the four repeated measurements. The dashedlines included on the plot represent curves of constant precision,indicating where fixed pattern noise is at a level that the precisionof the measurement ceases to improve with dose. Curves of 10%,3%, and 1% precision are shown. . . . . . . . . . . . . . . . . . . . 205

6.26 Normalized distribution of scaling factors for combining analog anddigital data from the Mixed Mode PAD. . . . . . . . . . . . . . . . 209

6.27 Distribution of pedestal offsets from one Mixed–Mode PAD detec-tor hybrid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

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6.28 Tomography of a section of a $1 bill illustrating the quantum ef-ficiency normalization distortion correction transform. Panel (a)shows the image original image, a merger of 10 100 second expo-sures using a Cu x-ray tube operated at 25 keV and 0.4 mA. Panel(b) shows the effect of applying the quantum efficiency normaliza-tion. There are a four dead pixels in the imager used to generatethis image. The same data set was used to generate these image aswas used to generate those shown in figure 6.29. . . . . . . . . . . . 216

6.29 Tomography of a section of a $1 bill illustrating the charge-shiftingadaptive filter correction transform. Panel (a) shows the imageoriginal image, a merger of 10 100 second exposures using a Cux-ray tube operated at 25 keV and 0.4 mA. Panel (b) shows theeffect of applying the adaptive filter correction. There are a fourdead pixels in the imager used to generate this image, these pixelsand their nearest neighbors are excluded from the adaptive filter.The same data set was used to generate these image as was usedto generate those shown in figure 6.28. . . . . . . . . . . . . . . . . 218

6.30 Estimation of the continuous exposure times required for a totaldose of 1 kGy(SiO2) for this Mixed–Mode PAD for three differentflux densities incident on the detector. These times are as calcu-lated based on equation 6.39 assuming that the flux density (Φ) in-cident on the detector is attenuated by 500 μm of silicon (the depththe Mixed–Mode PAD diode layer). Notably, these estimates do notinclude the additional protection the ASIC layer receives from thebump bonds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

6.31 Illustration of TID recovery mechanisms for SiO2 adjacent to thechannel of an nMOS or parasitic nMOS device. The two domi-nant radiation damage recovery mechanisms are tunneling, in whichholes tunnel directly through the SiO2 into Si and as such is stronglydependent on the distance between the trap and the channel, andthe thermal emission, in which holes are thermally emitted from lowenergy traps into the valance band of the SiO2 and drift towardsthe channel under the influence of fields in the oxide (assuming anactive device). Adapted from [68]. . . . . . . . . . . . . . . . . . . 230

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6.32 Silver Behenate diffraction (neg.) from a hybrid used in the Synchrotron-based radiation-tolerance experiment. Panel (a) shows a combina-tion of ten 1 s background images. Panel (b) shows a combinationof ten 1 s exposures of a Silver Behenate powder sample, with nobeam stop. The difference of panels (a) and (b) is shown in panel(c), where the intensity scale of the difference image is an order ofmagnitude smaller than that used in the exposure and backgroundimages. The radiation induced damage to the diode can be seen bythe 10 large (∼1 mm2) spots of greater intensity in the backgroundand exposure images, two in a column in the upper left quadrant ofthe image and eight in two columns of four spots in the upper rightquadrant of the imager. From left to right, by column of damagelocations, the exposure times were: (first column) 1440 s, 1920 s;(second column) 360 s, 30 s, 720 s, 960 s; and (third column) 60 s,120 s, 240 s, 480 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

6.33 Fractional leakage increase in primary beam region as a function oftime in the main, uncollimated, F2 beam, panel (a), and estimatedTID, panel (b). In the estimated TID plot, the point correspond-ing to 960 s was removed due to suspected beam fluctuations, asdiscussed in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . 234

7.1 Observed spectrum from 1 ms exposures of a single pixel withinthe Mixed–Mode PAD, operating at -35 deg. C, illuminated by anunfiltered Cu x-ray tube operated at a bias of 25 kV and 0.4 mA oftube current. A 75 μm pinhole mask was used to isolate the x-raybeam to the interior of the pixel so that charge sharing effects werenegligible. The spectrum of the Cu source will be dominated bythe Cu Kα characteristic emission line. However, there will alsobe a significant bremsstrahlung component extending up to thetube bias voltage of 25 keV. Because of this, it is very difficult todistinguish quantized Kα peaks beyond 0, 1, and 2 x-rays. . . . . . 240

7.2 Spectra of the acquired signal from a series of short exposures withMolybdenum x-ray tube, operated at 30 kV with 0.4 mA tube cur-rent and attenuated by a 791 μm Al absorber, collimated with a75 μm pinhole mask to restrict the beam to the interior of a singlepixel, thereby eliminating charge sharing effects. . . . . . . . . . . 242

7.3 Observed Poisson spectra for 1 ms integrations from a Cu rotatinganode source, monochromatized at the CuKα line at 8.05 keV. A 25μm pinhole mask was used to isolate the x-ray signal to the interiorof a single pixel, thus preventing charge sharing. Panel (a) depictsthe observed spectra, panel (b) shows the same result along with athree-parameter fit, where the scaling of the peak separation, thecommon width of each Gaussian peak, and the location of the zerox-ray peak are allowed to vary and be optimized. . . . . . . . . . . 244

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7.4 A wide-angle diffraction data set from a thin aluminium sheet isshown at increasing intensity scales from image (a) to image (d).An angular profile of this data is shown in panel (e); note that thevertical axis is logarithmic. The data set was acquired in a single,1 s exposure and clearly illustrates the large dynamic range of theMixed–Mode PAD. Both the signal of the attenuated main beam(shown in image (a) with a peak flux of 18 million x-rays/pixel/sec)and the sixth-order ring (shown just inside, though not at, the edgeof images (c) and (d) or as the 5th peak from the center in panel(e) with a peak flux of ∼700 x-rays/pixel/s) are clearly visible andmeasured with good statistics although they differ in intensity by afactor of more than 25,000. The dynamic range of the Mixed–ModePAD is, in fact, larger than this example would suggest, as evenfainter rings should also be observable with a larger-area Mixed–Mode PAD detector. . . . . . . . . . . . . . . . . . . . . . . . . . . 247

7.5 Panel (a) shows a zoomed in region of the Al WAX image from fig-ure 7.4, scaled to more clearly display the diffraction from higher-order harmonics passed through the monochromator. A quantita-tive description of this scattering is show in panel (b), indicatingan average intensity of 300 x-rays/pixel. What is remarkable aboutthis image is that it is possible to see such a weak signal so near tothe much more intense transmitted main beam and primary first-order diffraction ring. . . . . . . . . . . . . . . . . . . . . . . . . . 248

7.6 Single radiographic image of a Canadian dime taken with a Mo x-ray tube biased at 30 keV. The opposing face of the coin was filedoff to provide a clearer image and increase transmission. . . . . . . 250

7.7 Fine–sampled radiographic image of a Canadian dime taken witha Mo x-ray tube biased at 30 keV. The opposing face of the coinwas filed off to provide a clearer image and increase transmission. . 251

7.8 Comparison of magnified regions of figures 7.6 and 7.7. Panels (a)and (c) show sections of the single radiographic image, a portionof the sailboat jib and the right lower edge of the coin, selectedto highlight the effects of pixelation on the image. One dead pixelis evident by the black square in panel (a). Panels (b) and (d)show the same regions, respectively, fine–sampled to remove thepixelation effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

7.9 Image of the Thaumatin protein crystal used for the diffractionexperiments reported in this section. . . . . . . . . . . . . . . . . . 255

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7.10 Mosaic image of the diffraction pattern from the Thaumatin proteincrystal shown figure 7.9, when rotated through Δφ = 1 deg. in 1s. This image was made by combining sixteen separate images(i.e. tiles) of the same crystal rotation, acquired with the samesingle PAD hybrid at sixteen different detector displacements. Ineach tile a separate background image was subtracted and the tilesglobal scaling was adjusted to offset beam intensity variation. Theborder evident at the edge of each tile is due to a one pixel overlapregion between images. The data in this edge region is of poorquality due to the high edge leakage of the uncooled detector. Thiswas the first protein diffraction pattern taken with the Mixed–ModePAD. The image is shown to scale. . . . . . . . . . . . . . . . . . . 256

7.11 Annotated protein crystal diffraction stage at the CHESS F2 beam-line. Panel (a) illustrates the main components of this setup whilepanel (b) illustrates how the crystal is rotated to produce a diffrac-tion series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

7.12 Comparison of identical regions of a Thaumatin diffraction pattern,taken over a 1 deg., 10 s crystal oscillation, with a phosphor-coupledCCD system and the Mixed–Mode PAD. Panels (a) and (b) displaya series of lines of diffraction spots taken with a phosphor-coupledCCD system and the Mixed–Mode PAD (resp.). Panels (c) and(d) show background subtracted contour profiles of the second line,indexed from the top of the respective image, normalized to thepeak height of the brightest spot. The point of view for theseprofiles is taken to be along the vertical axis of panels (a) and (b)(resp.), in the positive direction. The missing 4th peak, indexedfrom the left, in the Mixed–Mode PAD line is due to a bad pixel. . 265

7.13 Comparison of an element from a canonical macromolecular dataset to the additional information revealed by fine φ-slicing a con-tinuous crystal oscillation. Panel (a) shows a frame taken with theMixed–Mode PAD containing a 1 deg., 10 s crystal oscillation. Inpanel (b), the same oscillation is divided into 50 frames and theintegrated intensity of one diffraction spot, as indicated in panel(a), is profiled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

7.14 φ-slicing on the same diffraction spot at differing levels of Δφ reso-lution: 0.2 deg., panel (a); 0.1 deg., panel (b); 0.05 deg., panel (c);and 0.02 deg., panel (d). This spot was produced by a Thaumatincrystal, with the intensity spread over 15 pixels on the detector,during a 1 deg., 10 s continuous exposure. . . . . . . . . . . . . . . 267

7.15 φ-sliced diffraction spot profiles, taken in Δφ = 0.02 deg. steps, fora series of different spots taken from the same Thaumatin crystal,in the same frame set. The form of the diffraction profile is echoedin each spot, as one expects since the profile reflects the underlyingstructure of the crystal. . . . . . . . . . . . . . . . . . . . . . . . . 268

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7.16 Change in the φ-sliced profile of a diffraction spot from a Thau-matin crystal before, panel (a), and after, panel (b), the crystalwas warmed from 100 deg. K to 170 deg. K at a warming rate of 6deg. K per minute. . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

7.17 95 ms exposure of SrTiO3 at the(0 0 1

4

)after a growth series, shown

if figure 7.18, near maximum diffuse scattering oscillation. Panel(a) is scaled to cover the entire range of the image, from 0 x-raysper pixel to 2,218 x-rays per pixel, while panel (b) is limited to showthe diffuse scattering, whose intensity is at most a few x-rays perpixel. Both images are shown in the negative and the intensity flooris set at twice the read noise (2σread) so that spots in the imagesactually represent 1 or more x-rays. . . . . . . . . . . . . . . . . . . 279

7.18 Homoepitaxial growth of a SrTiO3 thin film, as observed with theMixed–Mode PAD. Each peak in the reflected specular beam, panel(a), represents the completion of a single monolayer growth. Theaccompanying oscillations in the diffuse scattering are shown inintegral form in panel (b), while the time evolution of the diffusescattering profile are shown in panel (c). This last panel is plottedin the negative with the dark strip at the top of the image denotingthe location and extent of the specular reflection. Dashed verticallines are included in panels (a) and (b) to denote new material wasdeposited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

7.19 Histogram of the non-specular measurements measurements from asingle image within the SrTiO3 homoepitaxial growth series. Panel(a) shows the complete data set along with a fit to the zero x-raydistribution. Panel (b) shows the remaining data following a cutagainst pixels with no x-ray signal. . . . . . . . . . . . . . . . . . . 281

7.20 Diffuse scattering intensity profile near the first specular intensityminima. Panels (a) through (d) show how the profile improvesthrough merging frames, a combined effect of improved statisticsand cancellation of correlated noise effects within each frame. . . . 283

A.1 Example linear feedback shift register. . . . . . . . . . . . . . . . . 295A.2 Graphical descriptions how the generator Ω, as defined in equa-

tion A.2, splits vector space of 4-tuples with binary components,(Z/2Z)⊗ (Z/2Z)⊗ (Z/2Z)⊗ (Z/2Z). . . . . . . . . . . . . . . . . 297

B.1 Model used in current injection analysis. . . . . . . . . . . . . . . . 299

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LIST OF TABLES

3.1 Examples of prominent, worldwide, Pixel Array Detector projects.All x-ray referenced parameters assume an x-ray energy of 10 keV. 57

3.2 Imager specifications for the Mixed–Mode PAD. All x-ray refer-enced parameters assume an x-ray energy of 10 keV. The detectorframe rate given here is indicative of what is attainable from aMixed–Mode PAD hybrid; a camera implementation will be lim-ited by the rate at with the large quantity of data produced by theMixed–Mode PAD can be processed and stored. . . . . . . . . . . . 59

4.1 Summary listing of design specifications and expected performancefor the pixel front-end amplifier. . . . . . . . . . . . . . . . . . . . 71

4.2 Transistor sizing for the Mixed–Mode PAD integrator amplifier de-scribed in figure 4.4. The length unit of λ is a common VLSI scalingparameter intended to allow design to be easily migrated betweendifferent processes. For the TSMC 0.25 μm process λ = 0.12 μm. . 74

4.3 Thermal noise contributions from dominant amplifier noise sources.The Integrated column calculation assumes a 6 MHz bandwidth (tomatch the bandwidth of the sample and hold stage). . . . . . . . . 85

4.4 Flicker noise contributions from dominant amplifier noise sources.The Spectral column reports the value of equation 4.25 a 1 Hz. . . 85

4.5 Total noise contributions (RMS) from dominant amplifier noisesources. Combining these results yields a root mean square voltagenoise from all amplifier sources of 600 μV. . . . . . . . . . . . . . . 85

4.6 Summary of pixel diagnostic bits. Offsets are given in a big-endianformat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.1 Mixed–Mode PAD digital control signals. A line above a signalname indicates that the signal is active low. . . . . . . . . . . . . . 149

5.2 Summary of the elements of the Mixed–Mode PAD global envi-ronment register. This register contains the settings for the 6-bitDACs that control the reference voltages and bias currents usedthroughout the pixel array as well as additional bits that controlaspects of the detector’s behavior. More detailed information onthese register elements may be found in [7]. . . . . . . . . . . . . . 151

C.1 Mixed–Mode PAD prototyping submission history. . . . . . . . . . 301

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LIST OF ABBREVATIONS

ADC Analog-to-Digital Converter

ADSC Area Detector Systems Corporation

AFM Atomic Force Microscopy

ASIC Application Specific Integrated Circuit

CCD Charge-Coupled Device

CDS Correlated Double Sampling

CHESS Cornell High Energy Synchrotron Source

CSR Control Shift Register

CTF Contrast Transfer Function

ELT Enclosed Layout Transistor

ESR Edge Spread Response

ESRF European Synchrotron Radiation Facility

FPGA Field-Programmable Gate Array

GISAXS Grazing Incidence X-Ray Scattering

LCLS Linear Coherent Light Source

LOCOS LOCal Oxidation of Silicon

LSR Line Spread Response

MOSIS Metal Oxide Semiconductor Implementation Service

MTF Modulation Transfer Function

NSD Noise Spectral Density

OTF Optical Transfer Function

PAD Pixel Array Detector

PLD Pulsed Laser Deposition

PSF Point Spread Function

PSR Pixel Spot Response

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PSRR Power Supply Rejection Ratio

RHEED Reflective High–Energy Electron Diffraction

SEM Scanning Electron Microscopy

SEL Single Event Latchup

SEU Single Event Upset

SPICE Simulation Program with Integrated Circuit Emphasis

STM Scanning Tunneling Microscopy

STI Shallow Trench Isolation

TEM Transmission Electron Microscopy

TSMC Taiwan Semiconductor Manufacturing Company

TID Total Ionizing Dose

VLSI Very Large Scale Integration

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LIST OF SYMBOLS

A Amplifier gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

ADC Amplifier DC gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72

C Flat field correction map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Cdio Diode capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Ceff Effective capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Cgb Transistor gate-to-bulk capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Cgd Transistor gate-to-drain capacitance . . . . . . . . . . . . . . . . . . . . . . . . . 89

Cgs Transistor gate-to-source capacitance . . . . . . . . . . . . . . . . . . . . . . . . 89

Cint Integration capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Cneg Effective capacitance coupling VDDA to Vneg . . . . . . . . . . . . . . . . . . 89

Cpix Pixel input capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69

Cout Output capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Crem Charge removal capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Csh Sample & Hold storage capacitance . . . . . . . . . . . . . . . . . . . . . . . . 134

De Electron diffusion constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Dh Hole diffusion constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

ΔQ Charge removed per charge removal . . . . . . . . . . . . . . . . . . . . . . . . . 64

ΔQerr Error/uncertainty in charge removed during a charge removal 103

Δφ Crystal oscillation step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

E Electric field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

e− Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

EC Conduction band energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Edep Total x-ray energy deposited in a pixel during an exposure . 241

EG Band gap energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Ei Intrinsic energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

xxxv

EF Fermi energy/Fermi level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Etrp Trap energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

EV Valance band energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Ex X-ray energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

εSi Permittivity of Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Fa Fano factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

fnyq Nyquist frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

G Generator operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296

gabs Pixel absolute conversion gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

gdig Pixel analog-to-digital conversion gain . . . . . . . . . . . . . . . . . . . . . . 208

gds Transistor drain-to-source transconductance . . . . . . . . . . . . . . . . . 71

Ge Electron generation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Gh Hole generation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Gm Amplifier transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71

gm Transistor gate transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

gmb Transistor bulk transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . .76

gs Transistor source transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . 76

hdet Transfer function describing the total detector response . . . . .179

hdio Transfer function describing the diode impulse response . . . . 179

hpix Transfer function describing the effects of pixelization . . . . . . 179

θ X-ray angle of incidence on the detector diode surface . . . . . . . 32

I Identity operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Iaf Adaptive filter, charge shift corrected image . . . . . . . . . . . . . . . . 219

Ibuf Output buffer bias current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Idist Image with spatial distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Iflat Flat field image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Iioa Integrator amplifier bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Iqen Flat field corrected image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Isig Current from detector diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Itst Current from pixel test source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Je Electron current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Jh Hole current density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Jlkg Leakage current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

k Boltzmann constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Kα Kα fundamental emission line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Kβ Kβ fundamental emission line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

�pix Sample spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

�q Length scale of charge spreading in detector diode layer . . . . 179

λ X-ray attenuation length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

λSi X-ray attenuation length in Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

λSiO2 X-ray attenuation length in SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

μ Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

μe Electron mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

μh Hole mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

n Electron density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

NA Acceptor doping density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

ND Donor doping density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

ni Intrinsic carrier density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

NΔQ Count in in-pixel counter/Number of charge removals . . . . . . . .64

ξ Material ionization energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

p Hole density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

q Fundamental unit of charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

q|| In plane scattering vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Qint Charge collected in the pixel integrator . . . . . . . . . . . . . . . . . . . . . . 63

Qres Residual charge on integrator after charge removal . . . . . . . . . 103

Qtot Total charge accumulated during exposure . . . . . . . . . . . . . . . . . . .64

Rthm Annealing time constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

ρe Electron resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

ρfree Space charge density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

σread Detector read noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

T Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

tdrift Depletion region drift time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

texp Exposure duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Tsamp Spatial sampling period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

τe Free electron (conduction band) lifetime . . . . . . . . . . . . . . . . . . . . . 17

τh Free hole (valance band) lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

τrem Charge removal duration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Vbi Diode built in potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Vbn Bias potential for pixel integrator nMOS bias current source .91

Vbp Bias potential for pixel integrator pMOS bias current source . 92

Vcal Bias potential for pixel test current source . . . . . . . . . . . . . . . . . .123

Vcn Pixel integrator nMOS cascode bias . . . . . . . . . . . . . . . . . . . . . . . . . 92

VDDA Analog high supply potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

VDDD Digital high supply potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Vdio Diode potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Veqv Equivalent integrated potential to no charge removals . . . . . . . .64

VGNDA Analog ground potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73

VGNDD Digital ground potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Vhigh High reference voltage for pixel charge removal circuit . . . . . . . 98

Vlow Low reference voltage for pixel charge removal circuit . . . . . . . . 98

Vneg Amplifier inverting input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Voutc Comparator output potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Vouto Oscillator output potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Voutp Integrator output potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Voutsh Sample & Hold output potential . . . . . . . . . . . . . . . . . . . . . . . . . . . .122

Vped Pixel analog pedestal voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Vpix Pixel integrator virtual ground potential . . . . . . . . . . . . . . . . . . . . .63

Vpos Amplifier non-inverting input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

Vrb Diode reverse bias potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Vref Pixel integrator reference potential . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Vres Pixel analog residual voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

VT Transistor threshold voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Vth Pixel comparator threshold potential . . . . . . . . . . . . . . . . . . . . . . . . 64

Φ X-ray flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

φ Crystal oscillation angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

Φdio Transmitted x-ray flux through the detector diode layer . . . . 224

Φmax Maximum x-ray flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67

φrem Charge removal clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97

φrst Reset clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

wdio Diode depletion width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

ψs Surface potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Zout Open loop output impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Z/2Z Field of binary elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

ω1 Amplifier Unity Gain Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

CHAPTER 1

INTRODUCTION

When the microscope was first invented in the early 1600s, it opened up a win-

dow onto a new world of scientific discovery, revealing organisms on a scale that

had not been considered before. While remarkable, this feat was not unique as the

pattern of new scientific instruments spawning new scientific understanding is a

general paradigm that is repeated throughout the history of science. Particularly

in the 20th and 21st centuries, where access to high levels of technology has be-

come easier and more widespread, instrumentation has been a driving force behind

scientific advancement, with new instruments (like the electron microscope, space

telescopes, particle colliders, and many others) opening otherwise unaccessible

windows onto the universe and resulting in a proliferation of scientific knowledge.

Despite the impact of new scientific instruments, a focus on the development of

new instrumentation is not a widely acclaimed path for a physicist—offering little

of the exotic appeal of fields like string theory or cosmology. Consequently, one

sometimes encounters the bias that instrumentation is not a science but an exten-

sion of engineering. This view is rather limited, as it presumes the act of discovery

is decoupled from the thing that enabled that act. A well conceived instrument is

one that enables new scientific discoveries by virtue of its design; or, in other words,

because it enables scientists to look where it was not possible before and where

there are interesting things to discover. The latter portion of this point is quite

critical in distinguishing scientifically meritous instrument development from more

general engineering as it implies that the instrument developer appreciates where

opportunities exist for scientific discovery and that their instrument is designed to

realize these opportunities. It also implies that the instrument developer looks for

a multiplicative effect from the instruments they create, so that their efforts can

1

enable, through the application of the instrument by many scientists to a broad

field of questions, the creation of a body of scientific knowledge that will live long

past the instrument’s working life.

This thesis offers description and documentation on the development and first

applications of a new type of imaging detector for synchrotron based x-ray science,

the Mixed–Mode Pixel Array Detector (PAD). As will be argued in the remainder

of this chapter and those that follow, this work constitutes scientifically meritous

instrument development because it was designed with, and achieves, the objective

of opening an otherwise unaccessible window for scientific investigation onto, what

is expected to be, a very fertile field for scientific discovery.

1.1 X-Rays & Synchrotron Light Sources

X-rays have proven to be an extremely powerful structural and compositional probe

of matter spanning length scales from the macroscopic to the atomic. Evidence

of the utility of x-rays to science can be seen in the rapid development of sources

and techniques that followed Wilhelm Rontgen’s initial description of ‘a new kind

of radiation’ in 1895. In their earliest application, x-rays were used in radiography

to gain information about the structure of optically opaque objects. Yet, within

a decade after this initial report, it was discovered that they could yield composi-

tional information as well, when it was observed that gases exposed to x-rays emit

x-rays at lower energies, characteristic of their elemental composition. And before

two decades had elapsed, the first diffraction of x-rays from a crystal was observed,

extending the reach of x-ray research into the structure of matter on atomic length

scales. Since then, x-rays have played a critical role in some of the most impor-

tant scientific discoveries of modern times, including contributing significantly to

at least sixteen Nobel Prizes spread between the fields of Physics, Chemistry, and

2

Medicine.1

The achievements of x-ray science would not have been possible without steady

improvements in x-ray sources and detectors. In terms of x-ray sources, the goal

had been to develop successively more intense sources of radiation that allow

greater control over the spectral distribution of emitted x-rays. To measure the

signals produced by these, a vast array of detection methods have been developed

ranging from point detectors to two dimensional imagers, based on technologies

including, though not limited to x-ray film, photostimulable phosphors, geiger

counters, scintillator, and direct semiconductor detectors.

To appreciate what distinguishes the Mixed–Mode PAD from these previous

detectors and why it has the potential to enable a broad range of new x-ray science,

one must understand that the Mixed–Mode PAD is an x-ray imager designed for use

with a very unique source of x-rays, the synchrotron light source. A synchrotron

light source, often shortened to simply synchrotron, is a facility that produces

intense beams of x-ray radiation through the motion of ultra-relativistic charged

particles. This phenomena occurs when, at these extreme velocities, the standard

radiation field of an accelerated particle is Lorenz Transformed into the laboratory

frame of reference. Under this transform, radiation from the particle is beamed

into the direction of the particle’s motion, Doppler Shifting the spectra to higher

1(1901) W. Roentgen in Physics for the discovery of x-rays. (1914) M. von Laue in Physicsfor x-ray diffraction from crystals. (1915) W. H. Bragg and W. L. Bragg in Physics for crystalstructure derived from x-ray diffraction. (1917) C. Barkla in Physics for characteristic radia-tion of elements. (1924) K. Siegbahn in Physics for x-ray spectroscopy. (1927) A. Compton inPhysics for scattering of x-rays by electrons. (1936) P. Debye in Chemistry for diffraction ofx-rays and electrons in gases. (1962) M. Perutz and J. Kendrew in Chemistry for the structureof hemoglobin. (1962) J. Watson, M. Wilkins, and F. Crick in Medicine for the structure ofDNA. (1964) D. Hodgkin in Chemistry for the determination of the structure of penicillin andother important biochemical substances. (1976) W. Lipscomb in Chemistry for the determinationof boranes. (1979) A. Cormack and G. Hounsfield in Medicine for computed axial tomography.(1981) K. Siegbahn in Physics for high resolution electron spectroscopy. (1985) H. Hauptman andJ. Karle in Chemistry for direct methods to determine x-ray structures. (1988) J. Deisenhofer,R. Huber, and H. Michel in Chemistry for the structures of proteins that are crucial to photo-synthesis. (2003) P. Arge and R. MacKinnon in Chemistry for discoveries concerning channelsin cell membranes. (http://nobelprize.org)

3

energies creating a radiation source with, as we will see shortly, quite exceptional

characteristics [1].

The traditional method of x-ray generation, used since x-rays were first dis-

covered, has been through the vacuum tube. In these structures, electrons are

boiled off of a cathode into a vacuum, then accelerate through a strong (many kV)

electrical field until they strike the anode target. Within the anode, these highly

energetic electrons excite atomic transitions that give rise to characteristic x-ray

emission lines, whose energy depends on the material composition of the anode,

along with a background of bremsstrahlung radiation. Because x-ray production

via this technique is very inefficient (with more than 99% of the incident energy

converted to heat) these sources are fundamentally limited in the x-ray brilliance,

Brilliance ≡ photons/s

(mm2 source area)(mrad2)(0.1% bandwidth), (1.1)

by the heat load they are capable of imparting on the anode.

Synchrotron sources, on the other hand, exhibit intrinsic characteristics that

distinguish them, in terms of their spectra and brilliance, from the x-ray tube.

Because of their unique, and highly efficient, x-ray emission mechanism they can

provide very intense fluxes of x-rays over a relatively broad spectrum that, itself,

may be controlled through the speed and acceleration of the particles. The bril-

liance of these sources are only limited by the ability of the accelerator physicists

to control the beam dynamics and current, a science which they have been im-

proving upon steadily, achieving roughly an order of magnitude increase in photon

emission brilliance every four years [106]. In addition, because their high flux ex-

tends over a broad spectrum, it is possible to use x-ray optics to isolate the beam

within a selected energy bandpass. These two factors of high intensity and energy

selectabilty allow experiments to be performed that would be either impossible or

take excessive time with conventional x-ray sources [61].

4

While extremely useful, facilities to produce synchrotron radiation require a

large investment to build and maintain. Today, world-wide there exist over 70

synchrotron sources in various stages of planning, construction, or operation; rep-

resenting a combined investment of ∼$10B [40] where within the US alone the

annual operating budget of synchrotron facilities is estimated at over $200M [99].

Yet the utility of these facilities is evident in user base they support, which is

> 10, 000 scientists [40], covering an array of fields including Physics, Biology,

Materials Science and Engineering, as well as more unexpected fields, such as

Archaeology and Art History. This broad user base provides a field where new

detector technology can take root, sprouting new scientific discoveries.

1.2 Need for New Detectors

The investment into synchrotron technology and facilities that has taken place

from the 1960s (when synchrotron experiments were performed parasitically, op-

erating off of machines built for, and typically performing, particle physics experi-

ments) to today (when we are looking towards a fourth generation of synchrotron

light sources in facilities like x-ray free electron lasers and energy-recovery linear

accelerators) has resulted in tremendous increases in available x-ray flux. This

phenomenal growth has produced an abundance of x-ray flux, to the extent that

fluxes in excess of 1013 x-rays/s/0.1% ΔEE

are typical of modern beamlines. Yet

because a commensurate level of investment has not been made into x-ray detec-

tor technology, there is today a general concensus in the synchrotron community

that there exists such a gulf between the capabilities of synchrotrons to deliver

high photon fluxes and the capabilites of detectors to measure the resulting x-ray

signals that the detector is the limiting element in many experiments [99, 61].

A clear consequence of this gulf is that it is quite common in current experi-

5

ments to find experimenters attenuating their beam or a portion of the scattering

pattern because of the flux and well depth limitations of available detectors [61, 32].

In imaging detectors, the reason for this is a combination of the extended point

spread and limited dynamic range of the current generation of x-ray imagers. The

first property, the point spread, is the extent to which a signal incident at a point on

the detector is observed at other locations. In the presence of very intense signals

on the imager, an extended point spread can make it impossible to resolve weak

signals. In the case of the dynamic range, many systems studied at synchrotrons

have dynamic ranges that span many orders of magnitude (particularly diffraction

experiments). Because of their intensity, synchrotron light sources make accessing

signals in the weaker portion of this range possible, in principle, yet this is limited

by the dynamic range of which current imagers are capable.

A second, and arguably more serious, consequence of this gulf is that there

exists a broad range of time resolved phenomena that could be studied with cur-

rently available x-ray fluxes, but are not accessible because of the lack of capable

detectors for measuring these fluxes and framing at high rates [99, 61]. Today,

dynamic measurements using x-rays are either limited to point or 1D detectors for

continuous measurements or to the imaging of repetitive phenomena. In the latter

category, one requires cyclic systems or pulse–probe style experiments, where a

shuttering mechanism (either electronic or mechanical) is used to gate x-rays onto

the detector for times much shorter than the continuous frame rate. In this way,

these ensemble time resolved measurements are capable of building up a temporal

mosaic of the ensemble response of the system under investigation. This technique

suffers from the criticisms that: it is cumbersome and difficult, at least in cases

where a mechanical shutter must be used, are therefore is not widely used; and,

more seriously, that there exists a large class of dynamic systems that are inac-

6

cessible by these techniques because they do not conform to the limits outlined

above. In this class are many self–assembled growth phenomena where the diffi-

culties of exactly reproducing initial conditions make it impossible to temporally

tile multiple data sets.

Thus, the imager frame range, dynamic range, and point spread may be identi-

fied as areas where improving the imaging detectors available at synchrotron light

sources will expand the possibilities for x-ray science. The objective of the Mixed–

Mode PAD is to answer these three needs in a single detector by offering a device

capable of framing at continuous rates that are nearly three orders of magnitude

faster than what is attainable with current detectors, with a dynamic range nearly

four orders of magnitude beyond the capabilities of current imagers, and with a

point spread that is essentially limited by the pixel size of the detector. These ad-

vancements have the potential to not only improve science that is currently being

done but to enable new types of x-ray science, specifically continuous time resolved

imaging experiments on the ms timescale.

1.3 Document Organization

The body of this work is divided into five parts with the intention to divide the

discussion conveniently for different portions of its intended audience. Given the

length of this thesis, the author does expect that most readers would want to read

it from cover to cover. So the following is offered as a guideline to help readers

select what they might find interesting and relevant.

In the first part, encompassing chapters 2 and 3, a general background to pixel

array detectors is offered. This background reviews the methodology and physics

that underlies the operation of PADs, concluding with a historical review of PADs

preceeding and contemporary with the Mixed–Mode PAD.

7

In the second part, encompassing chapter 4, the design of the final Mixed–Mode

PAD pixel is presented and analyzed. This section is intended to help students

starting on new PAD designs by laying out the considerations that went into the

Mixed–Mode PAD pixel, while also providing a detailed reference on operation and

performance expectations of this pixel.

The third part, encompassing chapter 5, discusses the prototype camera built

for characterizing the hybrid detector performance. It is included mainly as a

background chapter for the characterization and experimentation work that follows

it, although it contains some control and readout timing information that should

be of interest to anyone working on a controller for this detector.

The fourth part, encompassing chapter 6, reports on the characterization of

the detector. This chapter is intended for those interested in understanding the

performance capabilities and limitations of the device. It also contains a section

discussing image correction algorithms that may be used to improve the quality

of the data from the Mixed–Mode PAD along with a discussion of how these

calibration terms may be measured.

The final part, chapter 7, presents results from the first experiments performed

with the Mixed–Mode PAD and is intended for the polymaths among the reading

audience.

8

CHAPTER 2

PIXEL ARRAY DETECTOR FUNDAMENTALS

Before embarking into the rough waters of the design, characterization, and first

experiments of the Mixed–Mode PAD, a basic understanding of what constitutes

a Pixel Array Detector is advised. In addition, to appreciate the design decisions

made, a familiarity with some fundamental aspects of semiconductor physics is

recommended. This chapter provides both of these by offering a discussion of the

general Pixel Array Detector methodology along with a comparison to contem-

porary synchrotron x-ray imagers so as to highlight the distinguishing features of

PADs. This is followed by a selective review of basic semiconductor physics with

an emphasis on topics relevant to the design and operation of a PAD. The chapter

concludes with a discussion of radiation effects on a PAD hybrid.

2.1 PAD Methodology

As discussed in the introduction the name Pixel Array Detector or PAD denotes a

broad class of x-ray detectors that incorporate custom signal processing electron-

ics into each individual pixel. For our purposes, PADs are two-layer hybridized

devices: one layer acts as a detector, directly converting x-ray photons into an

electrical signal, while the other layer contains custom electronics that process this

electrical signal. A grid of metallic interconnects, called bump bonds (commonly

indium or solder), join the individual pixels of the two layers. This configuration

is illustrated in figure 2.1.

This hybrid methodology distinguishes PADs from more conventional syn-

chrotron x-ray imaging devices by allowing them to directly detect x-ray photons

and immediately process the resulting signal with custom electronics. To see and

understand the impact of these features, it is useful to put our discussion in context

9

ASIC Layer

Bump Bonds

Diode Layer

Figure 2.1: Artist’s conception of a Pixel Array Detector (PAD) illustrating: thedetector diode layer, responsible for converting photons into electrical charge; thesignal processing application specific integrated circuit (ASIC) layer, responsiblefor processing the signal generated by the detector diode; and the array of bumpbonds that provide electrical interconnects between corresponding pixels on thediode layer and the ASIC. Thanks to Hugh Philipp for the image.

10

CCD

Phosphor ScreenOptical Taper

Visible Light X−rays

(a) Phosphor Coupled CCD

p+

n+

n−

X−

rays

Direct Convertion toCharge Carriers

(b) PAD Detector Diode

Figure 2.2: Comparison of the indirect method of x-ray detection used in phosphorcoupled CCDs with the direct detection approach of PADs. Panel (a) offers a cutaway of a CCD detector showing: the phosphor screen, that converts x-rays intooptical light; the optical taper, that collects and transits this light; and the CCDwhich quantitatively records the light. Panel (b) describes the detector diode layerof a PAD hybrid, illustrating: the uniform n+ region at the diode surface, usedto distribute the reverse bias voltage; the n− region in the detector bulk, wherex-rays directly convert into photocurrent; and the pixelated p+ regions at the baseof the detector where the photocurrent is collected. Neither figure is drawn toscale.

11

by comparing a PAD with the current workhorse of synchrotron x-ray imaging, the

phosphor coupled CCD.

Phosphor coupled CCDs were first developed for synchrotron science in the

late 1970s and early 1980s [42]. The scientific CCDs used in these devices exhibit

exceptional, nearly quantum limited, sensitivity combined with excellent stability

and linearity as well as a broad dynamic range [96]. As they would be ineffective

for imaging x-ray diffraction patterns directly, because of an x-ray transparent

active thickness, a thin phosphor sheet is used to convert the x-rays into visible

light. This light is then conveyed via an optical fiber taper onto the CCD, as

the cutaway of a typical phosphor coupled CCD shown in panel (a) of figure 2.2

illustrates. Reduction factors as high as 5:1 are commonly used to condense the

image of the phosphor screen, allowing a single CCD to span a substantially larger

active area while also facilitating the tiling of multiple CCDs together into a large

area detector.

While phosphor coupled CCDs are impressive devices, they do have a number of

limitations. First, the indirect x-ray detection method of an optically coupled taper

and phosphor screen drastically reduces efficiency of the detector, particularly with

the image reduction factors of the optical tapers commonly employed. As a result,

the signal yield of these systems is typically much less than a hundred e− per 10

keV x-ray.1 Modern CCDs are sensitive enough to make up for this low efficiency,

though only at the expense of the detector’s readout time—which is necessarily long

to maintain the required fidelity of the detector’s analog signal. As a consequence,

these detectors normally require a second or more of dead time to read out, limiting

their maximal frame rate to a fraction of a Hz.

In contrast, Pixel Array Detectors do not use an intermediate stage but rather

1For example, the ADSC Q270 (www.adsc-xray.com) reports an efficiency of 22 e− per 12 keVx-ray whereas the MAR USA SX-165 (http://www.mar-usa.com) reports 8 e− per 8 keV x-ray,with values taken from manufacture published spec. sheets.

12

collect the charge directly produced by x-ray conversion in the detector diode layer,

as illustrated by panel (a) of figure 2.2. This method yields roughly 2,700 charge

carriers (∼ 0.5 fC) for a 10 keV x-ray. The much greater charge yield produced by

direct detection relaxes the noise performance constraints needed to attain x-ray

quantum limited signal-to-noise performance. This in turn gives PADs a level of

design flexibility not enjoyed by phosphor coupled CCD systems. A clear illustra-

tion of this is in the processing technologies available for fabrication of PAD hybrids

in contrast with CCDs. To attain their exceptional level of sensitivity CCDs re-

quire dedicated fabrication lines with special processing steps. The PAD signal

processing ASIC, on the other hand, may be fabricated on commercial CMOS

fabrication lines in technologies with notably poorer noise performance than those

used to manufacture scientific CCDs. This offers a significant economic advan-

tage through the relative economies of scale. Specifically, due to the much higher

volume of CMOS device fabrication substantial infrastructure exists to support rel-

atively inexpensive prototyping while the variety of vendors and CMOS processes

available serves to lower the price of full-lot fabrications. Beyond the economic ad-

vantage, this level of signal also provides a design advantage in terms of the types

of signal processing that are possible. Unlike conventional x-ray imagers, which

are limited to aggregate measurements of the total signal yield, a x-ray detected

by a PAD yields sufficient signal to permit processing of individual photons [87].

Not all PADs take this approach, but the fact that it is possible illustrates the

great degree of flexibility offered by direct x-ray detection.

In addition to relatively poor efficiency, a second limitation of the indirect

detection method is the spatial spreading of the signal from individual x-rays.

Sometimes referred to as the point spread function, though this term technically

only applies in digital imagers whose analog impulse response is not degraded by

13

pixelation.2 Measured phosphor coupled CCD point spread functions typically

have an extent on the scale of mm at the 1% level [96]. In the direct detection

method of Pixel Array Detectors, the analog impulse response is determined by the

spread of charge carriers generated from individual x-ray conversion events. As will

be discussed in sections 2.2.1, 2.3, 6.3, and 6.4.4, the precise spreading of charge

carriers depends on a number of factors but under typical operating conditions

will be less than 50 μm. This tight spatial response makes it possible for the PAD

to detect weak signals in much closer proximity to intense signals than would be

possible with a phosphor-based synchrotron x-ray imager.

The final distinguishing feature of the PAD methodology that we will discuss

here is the capacity these imagers have for integrating pixel-level signal processing

electronics. Traditionally, x-ray detectors have been fixed-point analog integra-

tors with no capability to alter their behavior in-situ with an exposure [39]. The

advent of CCD based x-ray imagers changed this to a limited degree by offering

the ability to shift charge, effectively relocating the imager pixels, within an ex-

posure. As most commercially available CCDs are only capable of charge shifts

in one dimension, this technique has seen limited applications in x-ray imaging

[27, 108, 52]. More exotic CCD architectures allowing two dimensional shifts have

been developed and applied in other fields such as astronomy [18] and could find

application in synchrotron CCD systems, yet even this degree of functionality pales

in comparison to the possibilities of a modern PAD.

As previously mentioned, PADs are capable of integrating custom signal pro-

cessing electronics into each pixel. This degree of integration permits the creation

of smart pixels whose degree of functionality is predominantly limited by only the

area available within the pixel and the imagination of the designer. This assertion

2The classical definition of the point spread function assumes translational invariance of thedetector [54]. This presents a problem for pixelated devices if the pixelation breaks this symmetry.

14

is borne out by the wide variety of PADs that have been or are in the process

of being developed, including: digital counting PADs with energy discrimination

capabilities [71, 48]; analog integrating PADs with multi-frame memory integrated

into each pixel [85]; and high continuous frame rate PADs incorporating in-pixel

full or partial analog-to-digital conversion [76, 4].

Because of their unique hybrid methodology and its resulting distinguishing

characteristics of direct x-ray detection and in-pixel signal processing, Pixel Array

Detectors represent a new generation of x-ray imagers with a potential to greatly

advance synchrotron science. The remainder of this chapter focuses on the physical

principles permitting PAD performance, with particular attention given to the

effects of subjecting these devices to the intense radiation environment found at

synchrotron light sources.

2.2 PAD Semiconductor Physics

Understanding a complicated integrated circuit device, such as a Pixel Array De-

tector, is difficult without a few basic concepts in semiconductor electronics and

an understanding of how they are applied to produce selected semiconductor de-

vices. This foundation is necessary to understand the effects of radiation, both

wanted and unwanted, on these devices and to appreciate the steps taken to mit-

igate damaging effects. Towards this end, this section presents a brief review of

semiconductor physics, where the scope has been limited to elements that are di-

rectly relevant to understanding PAD performance and radiation hardness. A basic

background in semiconductor physics is assumed (e.g. band gap, intrinsic material,

Fermi Level, conduction band, valance band, etc.). Readers interested in a more

thorough discussion of semiconductor physics are referred to [97], [93], and [70].

15

2.2.1 Charge Concentration

Semiconductors are materials that exist in the gray area between conductors and

insulators. These materials exhibit a band gap (i.e. the energy separating the

conduction band from the valence band) small enough that at room temperature

there are a small, relative to a conductor, but appreciable, relative to an insulator,

number of carriers with enough thermal energy to enter the conduction band.

Control over the concentration of electrons in the conduction band and holes left

behind in the valance band is fundamental to semiconductor device physics. It

is accomplished through the introduction of ions (dopants) into the silicon lattice

that either supply electrons to the conduction band (donors, commonly antimony,

phosphorus, or arsenic), or bind an electron from this band leaving behind a hole in

the valance band (acceptors, commonly boron, aluminium, or gallium) [93]. These

dopants alter the Fermi Level (EF) of the semiconductor, changing the carrier

concentrations via:

n(x) = ni exp

{EF − Ei

kT

}, (2.1)

p(x) = ni exp

{Ei − EF

kT

}, (2.2)

where ni is the intrinsic carrier concentration, k is the Boltzmann constant, T

is temperature, and the Fermi Level (EF) of the intrinsic semiconductor is Ei =

EC+EV

2, where EC is the energy of the conduction band and EV is the energy of

the valance band [93]. The difference between the energy of the valance band and

the conduction band is the band gap of the material (EG = EC − EV).

2.2.2 Charge Transport

Charge transport within semiconductors influences many aspects of Mixed–Mode

PAD design and performance. Examples include the relationship between the high

16

voltage bias on the detector diode and the resolution of the Mixed–Mode PAD

(section 6.3) as well as the degradation of voltages held in the analog correlated

double sampling and sample and hold circuits (section 4.3.2). A discussion of the

basic charge transport properties of semiconductors follows.

The derivation of the charge transport equations within a semiconductor begins

with the current density ( Je and Jh) for electrons and holes, respectively, compris-

ing drift and diffusion components that describe the flow of electrons and holes

through the semiconductor [93],

Je = q (

drift︷ ︸︸ ︷μeEn+

diffusion︷ ︸︸ ︷De∇n), (2.3)

Jh = q (μhEp−Dh

∇p), (2.4)

where q is the fundamental unit of charge, n and p are the electron and hole

densities (resp.), μe and μh are the electron and hole mobilities (resp.), De and

Dh are the diffusion constants for electrons and holes (resp.), and E is the electric

field. Local continuity requires that

dn

dt+ ∇ · Je =

generation︷︸︸︷Ge −

recombination︷︸︸︷n

τe, (2.5)

dp

dt+ ∇ · Jh = Gh − p

τh, (2.6)

where Ge and Gh are the electron and hole generation rates (resp.) and nτe

and

pτh

are the electron and hole recombination rates (resp.), with τe and τh the elec-

tron and hole lifetimes (resp.). Combining these results gives the basic equations

governing charge transport in both depleted and undepleted regions of the semi-

conductor,

dn

dt=

diffusion︷ ︸︸ ︷De∇2n+

drift︷ ︸︸ ︷μe∇ ·

(En)

+

generation︷︸︸︷Ge −

recombination︷︸︸︷n

τe, (2.7)

dn

dt= Dh∇2p− μh

∇ ·(Ep)

+Gh − p

τh. (2.8)

17

As equation 2.7 indicates, these equations are composed of four terms: a diffusion

term, representing the thermal dispersion of non-equilibrium charge concentra-

tions; a drift term, describing the flow of charge under the influence of an external

electric field; a recombination term, representing the finite lifetime of these free

carriers; and a generation term, describing the spontaneous thermal or photonic

generation of free charge carriers.

A general, analytic, closed-form solution to these charge transport equations

does not exist. Typically systems with inhomogeneous or time varying electric

fields require simulations to be accurately modeled. Detailed simulators have been

developed [22] along with analytical approximations [13]. That said, there are a

number of illustrative special cases for which this problem may be solved analyt-

ically. The remainder of this section considers a set of these that will be useful

later in this thesis.

2.2.2.1 Generation and Recombination

If we assume that the generation rates for electrons and holes and the lifetimes of

these particles are homogeneous constants, then, if u is a solution to the homoge-

neous continuity equation, i.e. equation 2.5 or 2.6 with generation and recombina-

tion terms set to zero, one can show that

u′ = u exp

{− t

τe/h

}+Ge/hτe/h, (2.9)

is a solution to the inhomogeneous equation.

The electron and hole generation and recombination terms can vary depending

on the temperature and local energy band structure. However, as long as the

temperature is held stable and the local energy band structure remains constant,

this solution will be locally valid. As these constraints are expected to hold in the

cases of interest for this thesis, we will neglect generation and recombination terms

18

in the remaining examples—with the understanding that they may be reintroduced

to any subsequent solution by way of equation 2.9.

2.2.2.2 Pure Diffusion

Setting E = 0 in the generation/recombination-free form of the charge transport

equations, 2.7 and 2.8, yields the pure diffusion equation,

du

dt= D∇2u, (2.10)

where D is the diffusion constant. If we choose our initial condition to be u(x, 0) =

δ(x), the well known solution to this partial differential equation (PDE) is

u(x, t) =1

(π4Dt)32

exp

{− x2

4Dt

}, (2.11)

representing a Gaussian sphere of charge with RMS extent√

6Dt. As it is possible

to write an arbitrary initial distribution of charge q0(x) as

q0(x) =

∫d3x′ q0(x

′)δ(x′ − x), (2.12)

the linearity of the integration and differentiation operators allow us to use our

preceding result as a propagator to determine the time evolution of an arbitrary

initial state (q(x, t)). Thus,

q(x, t) =

∫d3x′ q0(x

′)u(x′ − x, t)

=

∫d3x′

q0(x′)

(π4Dt)32

exp

{−(x′ − x)2

4De/ht

}. (2.13)

A complete and detailed derivation of this result may be found in numerous sources,

such as [55].

2.2.2.3 Diffusion within a Constant Electric Field

This example is arguably the most useful result that we will derive as it offers

a good means by which to estimate the movement of non-equilibrium charge

19

(e.g. charge generated by x-ray conversion) in undepleted silicon and provides

a basis for approximating the behavior in depleted silicon.

To begin, note that, if we neglect recombination and generation terms, the

charge transport equations, 2.7 and 2.8, take the form

dn

dt= De∇2n+ μe

∇ ·(En), (2.14)

where for brevity we only explicitly present the electron results, as the hole result is

analogous. The influence of the arbitrary external electric field makes this problem

very difficult to generally solve in closed form. However, if we stipulate that

∇ · E = 0 and d�Edt

= 0 the problem reduces to

dn

dt= De∇2n+ μe

E · ∇n, (2.15)

then we find ourselves presented with a PDE that has the form of the convection-

diffusion equation,

du

dt= D∇2u+ c · ∇u. (2.16)

To solve this PDE, let u(x, t) be a solution to equation 2.11, the pure diffusion

problem. Employing the change of variables x → x′ = x + ct and expanding the

total time derivative of u(x′, t) into its partials gives

d

dtu(x′, t) =

∂

∂tu(x′, t) +

∂

∂x′u(x′, t)

∂x′

∂t

=∂

∂tu(x′, t) + c · ∂

∂x′u(x′, t)

=d

dtu(x, t) + c · ∇u(x, t). (2.17)

Since, by assumption, ddtu(x, t) = D∇2u(x, t) = D ∂2

∂�x2u(x, t) = D ∂2

∂(�x′)2u(x′, t) =

D∇2u(x′, t), substituting this result into equation 2.16 shows that our change of

variables is sufficient to turn a solution of the pure diffusion equation into a solution

to the convection-diffusion equation. For the particular problem of electron and

20

hole transport within a constant electric field, inspection shows us that c = μeE and

c = −μhE , respectively. Given an initial change distribution q0(x) we may use our

previous result, equation 2.13, to determine the time evolution of the distribution,

q(x, t) =

∫d3x′

q0(x′)

(π4Det)32

exp

{−(x′ − (x+ μe

Et))2

4Det

}, (2.18)

which can be interpreted as a collection of Gaussian spheres of charge drifting at a

constant rate of μeEq while expanding through diffusion to an RMS size of

√6Det.

An analogous treatment applies to holes.

2.2.2.4 Diffusion in a Linear Electric Field

Unfortunately equation 2.18 is not directly applicable to the problem of transport

in the depletion zone of a reverse biased junction diode as the fields in this region

do not meet the condition ∇· E = 0 due to the presence of ionized dopants exposed

by depletion. Within this region, under the uniform doping approximation which

we will discuss in section 2.2.3.1, the electric field increases linearly with depth into

the depletion layer [93]. A complete analytical evaluation of the charge transport

equations for this case is quite difficult and arguably unnecessary for the case

of greatest interest—the detector diode. Here our main concern is the spatial

distribution of charge carriers at the pixelated side of the diode (since integration

removes all temporal information). The results from the preceeding section are

still valid in the horizontal plane of the detector diode, perpendicular to the field

lines, so we may estimate the yield profile in these dimensions as a 2D Gaussian

where t in equation 2.18 is the mean transit time for a charge carrier through the

diffusion region under the influence of drift alone, given by:

tdrift ≈ w2dio

μVdio

ln{wdio

d

}, (2.19)

where wdio is the width of the depletion region, Vdio is the potential drop across

this region, μ is the mobility of the carrier type, and d is the depth into the region

21

at which the charge is released.

2.2.3 Basic Semiconductor Devices

There are two fundamental devices that need to be described in order to understand

the design of the Mixed–Mode PAD and the effects, both wanted and unwanted,

of radiation on this detector. These are:

• The P/N or diode junction.

• The MOS (Metal-Oxide-Semiconductor) capacitor.

Through the combination of these two basic components, one is able to build the

CMOS transistor which, in turn, is used to construct the complex electronics, such

as op-amps, comparators, counters and registers, that make up the Mixed–Mode

PAD.

2.2.3.1 P/N Junction Diode

The operation of the P/N junction diode is well known and detailed discussions can

be found in introductory semiconductor physics and analog electronics texts [14, 97,

93, 38]. Here, therefore, we present only a brief review of the P/N junction diode—

oriented towards topics that will be needed later. In particular, this discussion is

limited to the reverse bias mode of diode operation only, as this is the primary case

of importance for the Mixed–Mode PAD. Readers interested in a more complete

discussion of this device are directed to the references noted above.

A P/N junction diode is created when two semiconductor regions of differing

type share a common boundary. Considered separately, the Fermi Level (EF) of

each region is located in a different portion of the band gap, on opposing sides of

the intrinsic energy level (Ei). When a junction exists, however, a condition for

22

Figure 2.3: Energy band diagram of a reverse biased P/N junction.

static equilibrium is that the Fermi Level must be flat throughout the material.

To accomplish this, first, in the absence of an applied voltage, majority carriers

within each region diffuse towards zones of smaller concentration in the opposing

region, leaving behind space charge in the form of the immobile ionized dopants.

Following Poisson’s Equation this space charge will result in a static electric field

that, assuming that the x axis is normal to the boundary separating the two

semiconductor regions, is given by

∂2ψ(x)

∂x2=∂E(x)

∂x= −ρfree(x)

εSi

, (2.20)

where ψ(x) is the potential accompanying the field that leads to a bending of the

bands within the junction region, as illustrated in figure 2.3. Because this region

has a smaller majority carrier concentration than far away from the junction it

is called the depletion region of the diode. The total potential shift induced by

the junction is known as the built-in potential of the diode (Vbi). If an external

potential (Vrb) is applied in a manner so as to add to the potential difference

in the direction of the diode’s built-in potential, then this will result in further

enlargement of the space charge region and further band bending. Effectively, this

potential increases the separation of the bands on either side of the junction by

23

qVrb so that the total band separation becomes qVdio = q(Vbi + Vrb).

A parameter that is of great interest to PAD designers is the width of the

depletion region within the detector diode layer, as this value is needed to know

how to bias the detector diode to get full depletion with minimal parasitic leakage.

Under the typical diode slab model, where the doping concentration is assumed

to be uniform within the region on either side of the junction and undergo a

discontinuous change at the junction, the width of the depletion region (wdio) may

be approximated as [14]

wdio =

[{2εSiVdio

q

}{NA +ND

NAND

}] 12

, (2.21)

where εSi is the permitivity of silicon, NA is the density of acceptor dopants, and

ND is the density of donor dopants. For most diodes, in particular those used in the

Mixed–Mode PAD detector layer, one side of the junction receives a substantially

higher doping than the other. Supposing ND � NA the formula for the width

simplifies to

wdio∼=√

2εSiVdio

qND

=√

2εSiμeρeVdio, (2.22)

where ρe is the resistivity of the n-type region.3

From the width of the diode region it is possible to estimate the capacitance of

the diode (Cdio) via the simple formula

Cdio∼= εSiAdio

wdio

= Adio

√εSi

2μeρeVdio

, (2.23)

where Adio is the cross-sectional area of the diode. For integrating PADs, which will

be described in section 3.2, this capacitance is a crucial parameter as it provides

3The Mixed–Mode PAD detector diode is fabricated on high resistivity silicon wafers, reportedby the manufacturer to be 5 kΩ-cm to 10 kΩ-cm.

24

a path for the bias voltage of the detector to couple directly into the integration

node of the pixel, with a coupling magnitude given by

δVoutp =Cdio

Cint

δVdio, (2.24)

where Cint is the integration capacitance, explained in detail in section 4.2.1. Given

Cint, Cdio, and a noise figure for global fluctuation in the array, this formula sets a

limit on the fidelity required from the detector diode bias voltage, relative to the

reference voltage supplied by the pixel.

2.2.3.2 The MOS Capacitor

Because the gate of each CMOS transistor is ostensibly a MOS capacitor, under-

standing how this device operates is a prerequisite to understanding the operation

of the CMOS transistor. In addition, and more relevant to our application, the

explanation of this device’s operation underlies the explanation of how charge

trapping within the ASIC surface oxide, the dominant x-ray induced long-term ra-

diation damage mechanism, degrades the performance of CMOS devices. As this

topic is very thoroughly covered in many other sources ([97, 93]), this section is lim-

ited to a review, highlighting important results that will be useful elsewhere within

this thesis. Also, to simplify the discussion we will assume a p-type substrate, as

the results discussed here are analogous for n-type substrates, with appropriate

changes in the sign of relative potentials and charge.

The MOS capacitor may be likened to Neapolitan Ice Cream, consisting of

three stacked layer: at its base is the substrate wafer; above this is a silicon-oxide

passivation layer; and with the final layer, the gate, being either metallic (typically

Al) or highly doped polysilicon. Phenomenologically, changing the gate potential

alters the electric fields in the silicon di-oxide and the bulk silicon along with a

depth dependent local potential ψ(x), resulting in a redistribution of charge within

25

Figure 2.4: Semiconductor band diagrams depicting the accumulation, flat band,depletion, and inversion states of a p-type substrate. The parameter ψs representsthe surface potential induced by the applied voltage.

26

the semiconductor. If the applied voltage (V ) is written relative to the potential

of the bulk silicon, then four different charge distributions, illustrated in figure 2.4,

are distinguished:

Accumulation : V < 0, an excess of majority carriers (holes) is drawn to the

region of bulk silicon beneath the silicon di-oxide passivation layer.

Flat Band : V = 0, an aptly named distribution as there is no deformation of

the bands.

Depletion : 0 < V < VT (where VT = EF

qis the threshold voltage of the device),

the applied potential drives down the concentration of the majority carriers

(holes), depleting it below the thermal equilibrium level.

Inversion : VT < V , once the silicon/silicon di-oxide interface and adjacent bulk

regions are fully depleted, then an excess of minority charges are drawn into

this region. When the concentration of native minority carriers exceeds the

concentration of native minority carriers, which will occur when EF < qψ(x),

then the region is said to be inverted.

More rigorously, following the treatment given in [93], the local potential (ψ(x))

at a depth x into the semiconductor is given by equation 2.20 where the local charge

density (ρfree(x)) is given by the sum of the local free and space charge,

ρfree(x) = q [n(x) +NA − (p(x) +ND)] . (2.25)

The local free electron density (n(x)) and free hole density (p(x)) are in-turn given

by:

n(x) = ni exp

{q(ψ(x)− ψB)

kT

}, (2.26)

p(x) = ni exp

{q(ψB − ψ(x))

kT

}, (2.27)

27

where ψB = limx→∞ ψ(x) is the bulk potential. These equations (2.26 and 2.27) are

slight modifications of the standard charge carrier concentration forms (equations

2.1 and 2.2), with qψB replacing EF−Ei. This gives us a basic ordinary differential

equation (ODE) whose boundary conditions, stipulating that the capacitor gate

voltage (V ) is referenced to the potential of the bulk silicon, are ψ(x = 0) = V

and limx→∞ ψ(x) = 0. These equations show us how the voltage applied to the

MOS capacitor influences concentration of charge in the underlying silicon.

2.3 Radiation Effects in Silicon

For an x-ray detector, it goes without saying that one must understand the effect

of radiation to properly characterize and use the device. Generally, there are three

ways in which x-rays interact with matter [70]: 1) at the lowest energies, up to a

few keV, interactions are predominantly through the photoelectric effect. In brief,

this is when an x-ray interacts with an electron bound to an inner atomic orbital,

resulting in the absorption of the x-ray, the creation of a free electron with kinetic

energy nearly that of the incident x-ray as well as a vacancy (hole) in the electron’s

original binding location. 2) At higher energies Compton scattering begins to

dominate, this is when the x-ray elastically scatters from a free or loosely bound

electron, transferring a portion of its energy into kinetic energy of the electron

and recoiling at a lower energy. 3) Finally, at the highest energies, above 1.022

MeV, production of electron–positron pairs becomes important. Over most of the

spectral range where the Mixed–Mode PAD is designed to operate the photoelectric

effect is the dominant interaction mechanism, though at the highest portion of this

range the contribution from Compton scattering begins to be noticeable.

Both the photoelectric effect and Compton scattering produce highly energetic

δ-electrons [56]. Depending on where within the hybrid the interaction occurs, the

28

effect of the resulting δ-electron will vary. Broadly, we can distinguish three cases:

• X-ray absorption within the depletion region of a P/N junction.

• X-ray absorption within undepleted silicon.

• X-ray absorption within an oxide passivation layer.

In the first two cases, interaction in depleted and undepleted silicon, the δ-electron

produces a cloud of free charge carriers4 through ionization of local silicon atoms.

The quantity of charge yielded will be proportional to the x-ray energy (Ex) de-

posited in the detector as given by:

Q = qN = qEx

ξ, (2.28)

where Q is the generated charge, N = Ex

ξis the number of generated carriers, Ex is

the deposited energy, and ξ is the material ionization energy (for silicon ξSi ≈ 3.6

eV) [56]. The statistics of this generation process have been found to be better

that the√N expected of a pure Poisson process, presumably due to correlations in

the generation process [29]. To account for this, a term known as the Fano Factor

(Fa) is incorporated into the Poisson noise formula (RMS) so that

δQ = q√FaN, (2.29)

with Fa ≈ 0.1 in silicon [51, 101].

While the production of free carriers is very similar in depleted and unde-

pleted silicon, the impact of these carriers is markedly different. Two points in

particular distinguish the two cases. First is the matter of majority carriers. In

undepleted silicon, doping concentrations typically raise the level of free carriers

of the dominant species (i.e. holes in p-type material or electrons in n-type) to a

4The term free charge carriers is being used somewhat loosely here as shorthand to denotea conduction band electron or a valance band hole, as opposed to a carrier with kinetic energygreater than the work function of the material.

29

point that additional photo-ionization charge is insignificant by comparison. As a

result, only the minority carriers, which are suppressed under these circumstances,

may be detected and measured. In depleted silicon, there are effectively no free

carriers so that photo-signal from both species may, in principle, be observed. The

second point involves the charge transport mechanism dominant in these two cases.

In undepleted silicon, the electric fields are typically weak or non-existent so the

dominant charge transport mechanism is diffusion. In contrast, depleting silicon

requires electric fields to sweep away free charge carriers. These fields may either

occur naturally as with the built in field of an unbiased P/N junction or be imposed

externally. The presence of these fields shifts the predominant charge transport

mechanism from carrier diffusion to carrier drift. The phenomenological difference

between these two charge transport mechanisms was discussed in section 2.2.2.

When a δ-electron is produced within the oxide passivation layer of the hybrid

the result is very different. Here, the substantially greater separation of the con-

duction and valance bands effectively eliminates thermally generated free carriers.

As the mobility of electrons is relatively large (20 cm2/V·s at room temperature)

in comparison with that of holes (1.6 × 10−5 cm2/V·s at room temperature), the

presence of an electric field will rapidly sweep free electrons out of the oxide. Free

holes, on the other hand, will undergo much more gradual drift, often becoming

trapped at defect sites either in the oxide bulk or at the oxide/silicon interface [16].

As the lifetime of these trapped states can be quite long, though this is strongly

dependent on the temperature [8], over time this can lead to a charging of the

oxide that detrimentally affects the performance CMOS devices [3].

30

Att

enuat

ion

Len

gth

[μm

]

X-Ray Energy [keV]5 10 15 20

100

101

102

103

(a) Si Attenuation Length

Effec

iency

X-Ray Energy [keV]5 10 15 20

0

0.2

0.4

0.6

0.8

1

(b) 500 μm Si Diode Efficiency

Figure 2.5: Absorption properties of silicon. Panel (a) shows absorption length as afunction of energy. Panel (b) show the relative absorption efficiency of a 500 μm de-tector diode layer to normally incident x-rays. Values for these plots were obtainedfrom the Berkeley Lab, Center for X-Ray Optics web site (www.cxro.lbl.gov), whichin turn cites [46].

2.3.1 X-Ray Detection in the Mixed–Mode PAD

Hereto we have spoken about the effects of an x-ray conversion within various areas

of the PAD hybrid. Now, we shift our focus to the likelihood of this conversion and,

if it does, its likely location. To offer context for this discussion, we consider the

problem in terms of the detector diode. To an x-ray the diode is a block of silicon,

effectively indistinguishable from the rest of the hybrid, but from our perspective

this block of silicon has a specific purpose—to convert the x-ray into charge and

convey the charge to the signal processing electronics.

The detector layer of the Mixed-Mode PAD is effectively a monolithic P/N

diode. It is made from a 500 μmthick silicon diode with a light n- doping (∼ 1011

to 1012 donors per cm3 [26]). The face of the detector, towards the x-ray source,

receives a heavy n+ doping along with aluminization to provide an evenly dis-

tributed bias voltage, while the back of the detector receives pixelated p+ doping,

correspondent with pixels on the Application Specific Integrated Circuit (ASIC).

31

Figure 2.6: Model used for calculating the charge yield profiles of a monochromaticx-ray beam incident on a fully depleted silicon diode. The y = 0 plane is definedby the vertical plane containing path of the x-ray, while the the x = 0 plane isdefined to be the vertical plane perpendicular to the y = 0 plane, containing thepoint where the x-ray enters the diode.

When fully depleted, this architecture produces a vertical electric field that sweeps

charge carriers generated by x-ray conversion to the pixel integration stage.

The fraction of an x-ray beam of flux Φ absorbed in the Mixed–Mode PAD

detector diode layer is dependent on the energy and angle of incidence (θ) relative

to the surface normal. Generally, the probability that an x-ray will convert a

distance l into the detector layer is given by

P (l, E) =dl

λ(E)exp

{− l

λ(E)

}, (2.30)

where λ(E) is the x-ray absorption depth at the energy E. Figure 2.5 summarizes

the x-ray absorption properties of the Mixed–Mode PAD detector diode layer and

their dependence on energy.

As mentioned, the purpose of the detector diode is not only to absorb x-rays

but to convey the resulting charge carriers to the pixels for measurement. For

a monochromatic beam of x-rays, the profile of charge measured by the detector

will depend on the incident angle of the beam and the energy of x-rays within it

32

[μm]

Pro

bab

ility

Den

sity

[ 1 μm

]

-50 0 50 100 150 2000

0.01

0.02

0.03

0.04

0.05

(a) 4 keV (λ ≈ 10 μm)

[μm]P

robab

ility

Den

sity

[ 1 μm

]-50 0 50 100 150 2000

0.01

0.02

0.03

0.04

0.05

(b) 8 keV (λ ≈ 70 μm)

[μm]

Pro

bab

ility

Den

sity

[ 1 μm

]

-50 0 50 100 150 2000

0.01

0.02

0.03

0.04

0.05

(c) 12 keV (λ ≈ 230 μm)

[μm]

Pro

bab

ility

Den

sity

[ 1 μm

]

-50 0 50 100 150 2000

0.01

0.02

0.03

0.04

0.05

(d) 16 keV (λ ≈ 530 μm)

Figure 2.7: Charge yield profiles of monochromatic x-ray beams of differing energiesat incidence angles of 0, 5, 10, 15, and 20 deg. from the surface normal of a 500μm detector diode. The cutoffs exhibited in the 12 keV and 16 keV plots, panels(c) and (d), at high incidence angles are due to x-rays passing completely throughthe 500 μm thick diode layer.

33

in a manner that is relatively straightforward to calculate. From equation 2.30,

we know the probability of an x-ray converting a distance l into the detector

diode. As discussed earlier, this conversion results in a δ-electron that initiates a

complex cascade of secondary ionizations. It is generally assumed that the resulting

distribution of charge carriers may be described as a three-dimensional Gaussian,

q0(x) =Q0

π32σ3

r

exp

{−(x− x0)

2

σ2r

}, (2.31)

where Q0 is the total charge yield, x0 is the coordinate of the distribution center

of mass, and σr ≈ 0.012(E/1 keV)1.75 μm is a characteristic initial width of the

cloud [75]. From the discussion in section 2.2.2 we have a means to estimate the

time evolution of this charge profile as it moves through the depletion zone of the

detector diode. Combining equations 2.31, 2.30, and 2.18 gives:

p(x, y, E, θ) =

∫ zdetcos(θ)

0

q0(x0)dl

λ(E)πσ(l, θ)exp

{−(x− l sin θ)2 + y2

[σ(l, θ)]2− l

λ(E)

}, (2.32)

where

σ(l, θ) ∼=√

4kT

(z2det

Vdio

)ln

[zdet

l cos(θ)

], (2.33)

with all parameters as defined in figure 2.6 and equation 2.31. In figure 2.7, we

use this result to depict the normalized charge profile generated by monochromatic

beams of x-rays incident on the detector in the same location at varying angles of

incidence.

2.3.2 Radiation Damage

Conversion of x-ray photons into electrical charge within the detector diode is

a basic principle allowing PADs to operate. Conversion in other regions of the

hybrid, e.g. the diode depletions surrounding each transistor diffusion or within

the undepleted bulk substrate, tend rather to have detrimental effects on the de-

tector. Regarding photon induced radiation damage, two categories are typically

34

distinguished: single event effects, resulting from unintended x-ray conversion in

sensitive portions of the ASIC layer; and dose dependent effects that are the result

of the long term accumulation of damage within the detector [70].

2.3.2.1 Single Event Effects

Single event effects are exhibited as a change of state within the detector electronics

as a result of the burst of photocurrent that accompanies x-ray conversions within

the ASIC layer. Two types of effects are commonly distinguished: Single Event

Latchup (SEL) where a highly ionizing particle deposits enough charge in a small

volume to activate a parasitic thyristor [3]; and Single Event Upset (SEU) which

is manifest through an abrupt increase in the voltage of a node, or possibly nodes,

in the circuit resulting in a change of state within the device. SEL errors are

quite dramatic, resulting in the circuit entering into an inoperable state of high

current draw, potentially destroying the device [70]. Fortunately, if guard rings

and substrate contacts are used extensively throughout the ASIC layout then the

threshold for these errors becomes quite high, with tolerance up to 89 MeV-cm2/mg

reported by some sources in a 0.25 μm process [19]. SEU errors are more prevalent

and problematic with, as we will discuss, the potential to affect both digital and

analog circuitry.

SEU errors occur in digital circuits when an x-ray converts sufficiently close

to a transistor diffusion that the voltage on the node, at least temporarily, rises

high enough to change the logic state. This form of radiation damage can rewrite

registers, open gates, initiate logic sequences, and generally wreak havoc in a digital

design [70]. As with most radiation damage mitigation, deciding how to suppress

this damage involves a complicated matrix of design considerations. On one hand,

there are digital logic circuits that are designed specifically to perform robustly

in high-radiation environments. These architectures, however, entail a significant

35

cost in terms of area and design complexity [3, 70]. At a lower level of robustness,

there are certain logic families that offer improved protection (i.e. static logic,

where active elements retain logic states, as opposed to dynamic logic, where logic

states are held on capacitive elements that are periodically refreshed). While much

more compact than rad-hard logic circuits, there is still a trade off in terms of area

and power consumption for improved radiation tolerance. Particularly, due to the

limited area available within each pixel, care must be taken to weigh the costs and

benefits of these measures.

Regarding analog components the impact of single events is more subtle due to

the substantially larger capacitance typically found within these circuits and the

absence of a binary state. The result of these effects is seen primarily in the capac-

itive storage elements within the pixel and comes in the form of increased leakage

from switches connected to these nodes where charge is stored. The significance

of this current depends on the rate of x-ray conversion within the bulk silicon, the

area over which this charge may be collected, and the capacitance of these nodes.

While there is little one can do to affect the rate of x-ray conversion, apart from

operating at lower x-ray energies or finding a more efficient diode material, there

are steps that may be taken to mitigate the other effects.

The simplest mitigation measure is to increase the capacitance associated with

the analog storage elements. As previously noted, a 10 keV x-ray will yield roughly

0.5 fC of charge. If a 50 fF storage element is used and all this charge is collected

then the effect on the output is a 1% shift. Increasing the storage element ca-

pacitance 500 fF reduces this to a 0.1% effect. Where area and circuit bandwidth

limitations allow, increasing the capacitance of critical nodes is an effective, though

brute force, means to reduce single event effects. A much more elegant approach

that works well in conjunction with increasing the capacitance is to limit the col-

36

lection range for single event effects through the use of p− or n-wells. The fields

within the reverse-diode junction between the well and the substrate permits only

carriers of the substrate minority type to cross into the well. These carriers are,

for the same reason, prevented from passing through the reverse-diode junction

between well and transistor diffusion connected to the analog storage element. As

a result, the effective collection area for single event effects is reduced to the area

of the well. Some processes, such as the TSMC 0.25 μm, offer a deep n-well option

that allows a designer to imbed a large n-well into a p-type substrate in which

further p-wells may placed for fabrication of isolated n-type devices. Where this

option is not available, designers must rely on single type switches.

2.3.2.2 Long-Term Damage

Photons are, fortunately, much more forgiving, in terms of the types of radiation

damage that they induce, than massive particles. Unlike particles with mass,

x-rays do not induce persistent changes in the bulk silicon [70]. Instead, their

dominant long-term radiation damage mechanisms involve a gradual charging of

ASIC oxide layers through the creation and trapping of holes [70] and increases

in the leakage from the detector diode [14, 26]. These radiation damage effects

cannot be neglected, as they have the potential to seriously degrade the detector

performance if not mitigated through design [3]. Designing for radiation tolerance,

however, must be undertaken with care as the most robust techniques to mitigate

damage incur substantial costs in terms of area and may affect circuit performance

in ways that are difficult to model.

The trapping of holes in the oxide layer has an effect analogous to changing

the potential on the gate element of a CMOS capacitor, namely the trapped holes

induce electrical fields, which, in turn, alters the charge distribution in the un-

derlying silicon via the mechanism discussed in section 2.2.3.2. Depending on the

37

(a) Transistor Cross Section—taken along dashed line in panel (b)

(b) Transistor Layout Top View

Figure 2.8: Illustration of a sub-μm CMOS layout (shallow trench isolation) indi-cating regions susceptible to radiation damage. Panel (a) depicts a transistor crosssection taken along the dashed line indicated by the star encircled ‘a’ in panel (b),which, in turn, depicts the top view of a transistor layout. In both panels, re-gion 1 denotes where ionization induces transistor threshold voltage shifts, region2 denotes where ionization induces the formation of parasitic transistors betweenthe source and drain diffusions of a nMOS device, and region 3 denotes whereionization induces the formation of parasitic transistors in the field oxide.

38

location of this oxidation damage, these holes can either act as an effective gate,

applied commensurate with the actual gate of a transistor, or induce the formation

of parasitic transistors.

The flavor of silicon substrate (i.e n-type vs. p-type) also has a significant ef-

fect on the consequences of long term damage. In n-type silicon, accumulation

of holes trapped in the oxide draws majority carriers, electrons, to the surface

of the substrate. With a p-type substrate, the situation is reversed: here accu-

mulating damage repels majority carriers, driving the substrate under the field

oxide towards depletion and inversion. This discussion is expanded upon in figure

2.8, which distinguishes three oxide regions susceptible to radiation damage in a

deep sub-micron process, such as the 0.25 μm process from Taiwan Semiconductor

Manufacturing Company (TSMC) used to fabricate the Mixed–Mode PAD: 1) the

oxide separating the gate from the channel in both nMOS and pMOS devices; 2)

the oxide forming the passivation boundary at the edge of each nMOS transistor,

beneath the gate; and 3) the field oxide over the p-type substrate between n-type

diffusions from nMOS devices or n-wells.

In the first region, the effects of radiation damage are typically characterized as

shifts in the threshold voltage (VT) of the transistor. For nMOS devices, this shift

effectively lowers the threshold, resulting in increased channel current for a given

applied gate voltage. For pMOS devices this shift effectively raises the threshold,

leading to decreased channel current for a given applied gate voltage. As will be

discussed in more detail in section 6.7, the relationship between ionizing dose and

consequent threshold shift is non-trivial and strongly influenced by the presence

and strength of fields within the oxide, the thickness of the gate oxide, as well as

the temperature of the transistor.

In the second region, nMOS transistors are profoundly affected by the passiva-

39

tion technique used to isolate the deep sub-micron transistor structures. Known as

Shallow Trench Isolation (STI), this technique is commonly used in processes with

0.25 μm or smaller feature size. It differs markedly from the LOCal Oxidation of

Silicon (LOCOS) isolation used in larger-feature-size technologies and discussed

at length in previous PAD theses [83, 26]. In this technique, passivation trenches

descending 300-500 nm, with nearly vertical sides, are carved into the silicon to

form a boundary around each transistor, as depicted in the transistor cross section

depicted in panel (a) of figure 2.8. Along this surface, electric fields develop as dose

accumulates in the oxide, inducing the formation of parasitic channels between the

transistor source and drain. This effect is most significant at the corner where the

boundary oxide of the transistor meets the transistor gate oxide, because the in-

creased oxide volume relative to silicon volume, in this area, results in higher fields

with accumulating dose. These parasitic channels, that form along the edge of the

main channel between its source and drain, are typically modeled as independent

transistors, in parallel with the main transistor. Unfortunately, there are no di-

rect means to control these parasitic transistors with the gate voltage of the main

device. Consequently, as we will see later in this section, they can substantially

degrade the performance of, or even render useless, common circuit elements, such

as the simple current mirror.

In the third and final region, parasitic transistors may form in the field oxide

over any oxide covered p-type material, most commonly the substrate, between

any n-type diffusions (i.e. the source or drain diffusions of nMOS devices or an

n-well) of differing potentials. These parasitic transistors are known as field-oxide

transistors or FOX transistors and tend to be less significant than the parasitic

edge transistors that form in the second region. There are multiple reasons for this.

First, the effect of these parasitic devices can be partially or completely mitigated

40

through the placement of substrate contacts within a layout, so that basic practices

of good mixed-signal layout will protect against this problem. Second, minimal

transistor spacing rules cause these devices to be relatively long. Finally, the

structure of the STI passivation results in a somewhat circuitous path that current

must follow in these parasitic devices. Despite the typically lower significance,

consideration of the effect of parasitic field-oxide transistors should not be neglected

as it is easy to lay out structures in which these parasitic devices can become quite

problematic.

As with transient radiation damage, the methods commonly used to mitigate

long-term damage span a spectrum of trade-offs between effectiveness and cost, in

terms of area, power, and complexity. At one extreme, it is possible to use special,

rad-hard foundries such as those operated by Lockheed-Martin in Manassas, VA or

the Honeywell Solid State Electronics Center in Plymouth, MN. These foundries,

though, tend to be hard to gain access to and produce devices with lower yield and

performance characteristics roughly one generation behind the current generation

of commercial CMOS electronics [19]. Fortunately, it has been shown that a large

degree of radiation tolerance may be attained by selecting an appropriate process

for the design [58, 92]. Studies of commercial CMOS processes carried out as

part of the Large Hadron Collider (LHC) detector development effort observed

that radiation tolerance effects first seen in thin MOS capacitors [43] extended

to processes with smaller feature sizes [19]. The effect is explained by noting

that, as feature size decreases, the thickness of the gate oxide decreases as well.

Decreasing oxide thickness will improve device radiation tolerance as there will

be less material for x-rays to convert in, with the shift in threshold voltage per

Mrad deposited in the oxide falling off roughly proportional to the square of the

oxide thickness. However, below a gate oxide thickness of ∼ 10 nm an additional

41

Enclosed Layout Transistor

Linear Transistor

Drain

Source

Gate

Drain

Gate

Source

Figure 2.9: Illustration of an Enclosed Layout Transistor (ELT) in contrast to thetraditional linear transistor.

reduction is gained [19].5 This additional radiation hardness is thought to be due

a reduction in the mean lifetime of holes trapped in the silicon di-oxide as a result

of recombination with electrons tunneling into the oxide from either the gate or

channel regions.

While process choice is very effective in mitigating radiation induced transistor

threshold shifts, it is less effective in preventing the formation of parasitic transis-

tors. Other methods must be employed to deal with these. The most costly, in

terms of area consumed, and brute force methods available for standard CMOS

technologies involves transistor layout techniques [92]. Most commonly a layout

approach known as enclosed layout transistors (ELT), illustrated in figure 2.9, is

used to prevent the formation of parasitic transistors by eliminating any paths

between an nMOS device source and drain that are not controlled by a section of

the transistor gate [2]. Use of these devices is not without cost. ELT devices tend

to take up more area, require larger effective W/L ratios, and are more difficult

to model than standard linear devices. The cost in terms of area of this layout

approach along with the uncertainty it introduces into circuit modeling means that

5For context the gate oxide of a 0.25 μm process, as used in the Mixed–Mode PAD, is 5-7 nm.

42

its use within a PAD pixel design should be judicious.

More recently a new, linear, radiation-hard structure was reported in [92].

Transistors based on this report were designed and characterized by Dr. Alper

Ercan, a former member of the Cornell PAD development group, and are presented

in detail in his thesis [26]. As Dr. Ercan’s vetting of the linear, radiation-hard

transistor was not completed in time to incorporate them into any Mixed–Mode

PAD submission, we will only review the basic idea of this transistor structure

here. Readers interested in a more thorough discussion are referred to the two

sources above.

The idea behind the linear, radiation-hard transistor is to remove the oxide at

the edge of the nMOS device by encircling it with bulk silicon. This is done with

standard fabrication design tools by extending the gate and active area to cover

the region around the edge of the transistor, including surrounding the source and

drain diffusions. Now, this structure is effectively a larger transistor than we desire,

formed from the linear transistor directly between the source and drain diffusions,

and secondary transistors at the edges of this device, due to the gate over the active

boundary region. One gets back the performance of a linear transistor (i.e. perfor-

mance that can be characterized by the W/L ratio between the source and drain)

by using a n+ select masks in the desired active transistor region and a p+ select

mask in the boundary region. For our purposes, the effect of the n+ select mask

is to cause the polysilicon gate in the region it covers to receive a n+ doping. This

doing induces a small positive gate voltage, effectively reducing the threshold volt-

age in the region directly between the source and drain diffusions. Similarly the p+

select mask causes the polysilicon in the region bounding the transistor to receive

a p+ doping that acts as a small negative gate voltage, effectively increasing the

threshold of the secondary devices in the boundary region. The difference between

43

Vdd

Vout

M1

M2

M3

M4

ICP

ICN

IBN

Vin

(a) Cascode

Vdd

Vdd Vdd

Vout

M1 M2

M3M4

M5

M6 M7

M8M9

M10 M11 M12 M13

VposVneg

IBP

ICP

ICN

(b) Mirror Cascode

Vdd

Vdd Vdd

M0

M1 M2

M3 M4

M5 M6

M7 M8

M9 M10

IBP

IBN

ICN

VposVneg

Vout

(c) Folded Cascode

Figure 2.10: Three amplifier architectures offering similar performance character-istics but drastically different levels of radiation tolerance. Amplifiers are orderedfrom left to right in order of increasing radiation tolerance.

these effective gate voltages, ∼1 V (the Si bandgap) assuming both the n-type and

p-type polysilicon are heavily doped, acts to suppress channel formation outside

of the region directly between the source and drain diffusions. As a result, for

low gate voltages, this technique effectively yields a linear device that is radiation

hard to 100s of Gy TID(SiO2).6 This device is not without its drawbacks, though.

Foremost among these is the fact that, if the gate is raised high enough, then these

secondary transistors in the boundary will become active at a significant level.

This can present a leakage problem unless the region around the boundary gate is

protected by a guard ring. Consequently, this layout technique enlarges the area

required for the device by the bounding gate and guard ring at the perimeter of

the device. In addition, the larger gate area increases the capacitance of the gate

node while the secondary transistors distort the channel current vs. gate voltage

curve of the device. Because of these effects, this layout technique is certainly not

a silver bullet for the problem of radiation damage; however, as we will discuss in

more detail in chapter 4, there are areas where it could find useful application.

An alternative approach to radiation hardness involves choosing circuit archi-

6See the discussion on units and dose in section 6.7 for an explanation of this terminology.

44

tectures that are inherently more resilient to long term radiation damage. This

concept has long been used in radiation hard digital design, where combinatoric

logic circuit elements (e.g. redundant latches with a majority voter logic output)

are commonly used in radiation hardened designs to protect against single event

upsets [70, 102]. While discussion is essentially absent in the literature, the idea of

radiation tolerance through circuit architecture extends to analog devices as well.

To illustrate this point, consider the three amplifier topologies shown in figure

2.10, which represent three generations of the front-end amplifier used in PADs

produced by the Cornell PAD development group.7

The cascode structure shown in panel (a) of figure 2.10 is, by far, the most

susceptible to radiation damage. Specifically, any threshold increase induced by

radiation in transistor M1 will translate directly into a decrease in the quiescent

voltage of the amplifier output. In addition, and probably more significant, in-

creases in the channel current of transistor M4, the dual effect of radiation-induced

lowering of the threshold of this device and parasitic channels formation around

the edges of this device, will lead to greater current flow through the device at a

given bias voltage, resulting in an additional lowering of the quiescent voltage of

the amplifier output.

The mirror cascode architecture shown in panel (b) of figure 2.10 is much more

radiation tolerant due to its use of a differential topology. Unlike the cascode ar-

chitecture, the differential pairings in this device, and consequent common mode

cancellation, means that only differences in accumulated dose effects will shift the

quiescent output voltage of the amplifier. This particular architecture, however,

suffers from its use of nMOS current mirroring stages (transistors M10, M11, M12,

and M13). These current mirrors become, gradually, less effective as parasitic tran-

7The cascode architecture was used in the integrator for the original 100×92 μs imager [83],while the mirror cascode was used in the larger area redesign of the μs imager in the TSMC 0.25μm process [26], while the folded cascode is used in the Mixed–Mode PAD.

45

sistors form along their edges, stealing current from the gate controlled portion of

the device. This current loss degrades the transconductance of the diode con-

nected component of the mirror, ultimately degrading the frequency response of

the circuit and potentially leading to device instability under some feedback con-

figurations. In principle this effect could be reduced by increasing the length of the

transistors in the mirror. However, this will come at the expense of the amplifier

frequency response, as any increase in L will either reduce the transconductance of

transistors M11 and M12 or require a proportional increase in W thus increasing

the capacitance of the gate node. Consequently, if circuit performance is not to be

sacrificed, this design requires an ELT layout for true radiation hardness.

The final design, the folded cascode shown in panel (c) of figure 2.10, is the

most intrinsically radiation tolerant as a result of its differential architecture and

the fact that the two sets of nMOS devices present (transistors M7 and M8, along

with M9 and M10) are both very tolerant to the formation of parasitic transistors.

In the case of the pair of bias devices (transistors M9 and M10) they operate with

a constant gate voltage and therefore may be lengthened to minimize the impact of

parasitic devices without degrading the performance of the circuit. In addition, to

the extent that parasitic devices do form along the edges of these transistors, their

effect is minimal as, as with the Mirror Cascode, only the difference in parasitic

leakage will affect the quiescent output voltage of the amplifier. The cascode

devices (transistors M7 and M8) are both source driven so they do not exhibit the

same loss of control seen in gate driven devices. Hence, the effects of radiation on

this architecture are minimal compared to the other architectures presented.

To achieve a robust yet compact pixel, the Mixed–Mode PAD incorporates a

combination of these radiation damage mitigation techniques. In chapter 4, where

the design of the Mixed–Mode pixel is presented in detail, we will offer a discussion

46

of the particular steps taken to protect individual components of the pixel against

radiation damage. Finally, in chapter 6, we will present measurements of the

radiation tolerance of this imager.

47

CHAPTER 3

MIXED–MODE PAD PREHISTORY

For a new graduate student starting on a detector design project like the Mixed–

Mode PAD, it is easy get the impression that this project is a unique radical

departure from what has gone on before. In reality, though, this project is better

described as a continuation and extension of a much larger body of work. Before

delving into the details of the Mixed–Mode PAD architecture, it is useful, then, to

spend a few pages looking at where this design came from. This prehistory offers

a context for the design decisions that went into the Mixed–Mode PAD as well as

credit to those individuals whose hard work made it possible for this project to

achieve what it has.

In the early days of Pixel Array Detector development, the x-ray detector

R&D community divided itself along two distinct paths: Analog Integrating PADs,

which operate by collecting charge on an analog storage node—conceptually similar

to a Charge-Coupled Device (CCD) imager; and photon counting Digital PADs,

which use a discrimination circuit to count individual x-rays. These approaches

each entail unique challenges and offer distinct advantages. It was the desire to

combine the advantages of these two approaches that led in 2003 to the genesis of

the Mixed–Mode PAD project, a collaboration that grew from the multi-framing

Analog PAD project at Cornell and an attempt to develop a pure Digital PAD at

ADSC [4].

More broadly, though, the Mixed–Mode PAD project finds its origin in the

development of Scientific CCD imagers and Silicon Pixel Detectors for Particle

Physics that occurred in the later part of the 20th century. By offering two possible

starting points for developing x-ray imagers, these sources can be seen as the cause

of the division between Digital and Analog PADs. As the following sections will

49

illustrate, the capabilities of the detectors that sprang from these two origins are

quite distinct, to the point that both have broad and separate ranges of applications

at which they excel. Because of this, the confluence of these two approaches in the

Mixed–Mode PAD has yielded a new type of detector with capabilities that are

distinct from these predecessors.

3.1 Digital Pixel Array Detectors

Digital Pixel Array Detectors or photon counting Pixel Array Detectors are so

called because their data is quantitized into a digital format immediately upon

the acquisition of each x-ray photon. Their circuit architecture typically comprises

three primary stages:

• An analog pulse shaping stage that acts to bandwidth limit and amplify the

detector diode signal.

• A discrimination or thresholding stage that determines when a sufficient level

of signal is observed.

• A recording stage that counts the number of discriminator triggers.

This approach is, by far, the most popular, having been pursued by numerous

groups [71, 22, 12, 48]. Perhaps the reason for this popularity is rooted in the

fact that the first hybridized detectors followed this model. These predecessors

of the x-ray photon counting Pixel Array Detectors were Silicon Pixel Detectors

developed for the vertex tracking chambers of large particle physics experiments,

e.g. ATLAS, CMS, and ALICE at the LHC [104]. Since beginning in the 1980s,

research into Silicon Pixel Detectors has proven very successful in overcoming rate

limitations and improving spatial resolution in increasingly energetic and complex

particle collider events [87]. The research that came out of these projects can be

50

credited with creating the hybrid detector concept and inspiring the Digital PAD

development that began in the 1990s.

Yet, while Digital PADs were modeled after Silicon Pixel Detectors, the experi-

mental constraints and detector requirements of vertex tracking in a collider-based

particle physics experiment are very different from those of synchrotron x-ray ex-

periments. In a vertex tracking chamber, the choice of a digital over analog ap-

proach is one necessitated by the large quantities of data produced by every event

and the necessity to sparse this data at the earliest possible stage. Particle physics

experiments assume that, in each event, only a small number of particles, typi-

cally zero, will deposit signal into a given pixel. At the same time, the amount

of deposited signal varies depending on the particle’s type and path as it passes

through the pixel, so the intensity of this signal needs to be recorded [87]. In many

synchrotron x-ray experiments, a monochromatic x-ray beam is used so the de-

posited signal per-x-ray is known to within a small range of variation, as explained

in section 2.3, and the number of x-rays observed during an exposure by a pixel

can be in the millions.

Because of these different experimental requirements, adapting the Silicon Pixel

Detector approach for Digital PADs has involved evolving the pixel back-end into

a counter along with a circuit to prevent retriggering on the same photons. The

resulting Digital PAD circuitry, specifically the front-end pulse shaping and back-

end retrigger prevention electronics, entail a processing time for each x-ray photon

that creates dead time in each pixel, suppressing the observed flux relative to

the actual flux. This dead time is one of the main limiting factors for Digital

PADs as it sets an effective flux limit on the device. Typically, Digital PAD

papers report a flux limit of ∼ 107 x-rays per pixel per second [12, 48]; however,

this value is somewhat misleading, as it reflects a theoretical flux limit calculated

51

based on the shaping time and processing time of the pixel with assumed source

statistics. As x-rays are not uniformly distributed in time, the observed number

of events needs significant correction at fluxes within a few orders of magnitude

of the quoted maximum. As the actual flux approaches the maximal flux, the

dead time correction factor increases rapidly, typically exponentially, along with

the uncertainty introduced by this dead time correction. Accurate dead time

corrections within an order of magnitude of the flux limit require extremely careful

characterization of the x-ray source, particularly in the case of synchrotrons where

the x-rays do not obey a true Poisson distribution due to the underlying structure

of electron bunches within storage ring.1 From an experimental standpoint, the

flux limit translates into a restriction on the detector’s dynamic range for a given

time scale. As an example, if we assume a practical flux of 106 x-rays per pixel per

second and require a measurement with 1% statistics, then a 100 ms integration

would only yield one decade of dynamic range. These considerations do not arise

in event-driven particle collider experiments since the per-pixel signal levels are so

much smaller.

Despite these limitations there are a number of distinct advantages that the

photon counting Pixel Array Detectors offer over their analog integrating coun-

terparts. Foremost, as these are discriminating devices they possess an energy

threshold associated with their discrimination level. This gives them a natural

ability to reject x-ray fluorescence as well as any Compton background present in

the beam. Additionally, in these devices, the well depth grows exponentially with

the amount of pixel area devoted to storage, as opposed to the linear growth one

finds in most analog integrating systems, which is particularly notable because this

1As an example to illustrate this point consider the typical bunch timing at the Cornell HighEnergy Synchrotron Source. Here bunches are ∼ 56 ns in duration with either 280 ns or 294 nsbetween the start of successive bunches. Because of this timing structure a Digital PAD shouldalways see two photons in successive bunches but never see two photons in a single bunch.

52

increase in well depth does not come at the expense of precision, as the front-end

gain remains fixed. Also, once digitized, the data from the pixel is effectively im-

mune to noise yielding a very high signal to noise ratio that is only very weakly

dependent on integration time.2 Because the data is already in digital form, it

may be read off the detector very rapidly. Finally, Digital PADs typically do not

need to be cooled for operation at low count rates.

3.2 Analog Pixel Array Detectors

Analog PADs can be seen as the indirect descendents of the scientific CCDs that

were adapted for use with x-ray sources in the 1980s and have since become the

standard in imaging at synchrotron x-ray sources. Primarily advocated and de-

veloped by the Gruner Detector Group at Cornell University, a group which origi-

nally specialized in x-ray CCD development, Analog PADs adopt the fundamental

methodology of CCDs. As descendants of CCDs, they collect photocurrent as a

quantity of charge on an analog storage element, retaining this analog quantity

until it is digitized after the exposure ends. However, the CMOS Very Large Scale

Integration (VLSI) based signal processing electronics available to Analog PADs

offer functionality that goes far beyond what is possible in CCDs. Rather than the

complicated clocking schemes used to shift charge through and off of CCDs, Analog

PADs integrate signal processing electronics at the pixel level. This integration has

allowed such variety as detectors with multiple memory elements in each pixel for

microsecond framing [83], massively parallel in-pixel analog-to-digital conversion

for high frame rate operation [76], and nearly continuous framing though the addi-

tion of a sample-and-hold stage operating independently of the signal integration

electronics [25]. Still, what all Analog PAD architectures possess in common is an

2With the exception of the possibility of single event upsets, as discussed in section 2.3.2.

53

integrating front end and, as such, they exhibit performance characteristics that

differ significantly from the Digital PADs, discussed in the previous section.

Perhaps the most dramatic difference between Analog and Digital PAD method-

ologies is the maximum flux per pixel these devices can tolerate. Because Analog

PADs process current, rather than discriminating photons, their behavior is de-

termined almost completely by the response of the pixel front-end electronics. As

the Analog PAD front end integrates currents most signal transients are smoothed

out as long as their duration is short relative to the length of the exposure. Hence,

generally, the maximum flux per-pixel is limited only by the bias current of the

integration stage amplifier, allowing the Analog PAD methodology to exhibit very

high per-pixel flux tolerance. This tolerance has been experimentally verified with

groups reporting using these detectors at per-pixel fluxes as high as 1012 x-rays

per second [86], five orders of magnitude higher than the optimal performance of

Digital PADs.

While the flux capabilities of Analog PADs are impressive there are also signifi-

cant drawbacks to this detector methodology. First, converting the acquired signal

to a digital value and recording this takes a certain amount of time. With the ex-

ception of analog pixel architectures which incorporate very high degrees of parallel

digitization (e.g. the Analog PADs, mentioned earlier, that incorporate Analog-to-

Digital Converters (ADCs) into each pixel have been designed for a frame rates of

120 Hz [76]) there is, in general, a fundamental trade-off between the detector’s

speed, well depth, and precision in an optimized analog detector. This trade-off

arises from the fact that detectors storing acquired signal in an analog element are

limited by the span of that element, e.g. the depletion voltage of a CCD, so that

setting a front-end gain sets the well depth. To achieve a larger well depth one

can reduce the gain of the front end; however, to keep the same sensitivity, the

54

precision of the readout electronics must increase, which, in turn, requires longer

settling times and, therefore, a slower readout. Because of the precision required

in their readout and their large number of pixels, typical readout time for Analog

PADs are on the order of a second—making high continuous frame rate operation

difficult to achieve.

A second significant drawback, alluded to earlier, is the relation between well

depth and pixel area. Generally Analog PADs use a linear capacitive charge storage

element to set the system gain.3 Because of this the well depth, and consequently

the absolute dynamic range of the pixel, is strongly limited by the size of the pixel.

As an example, typical sub-micron processes offer capacitors with capacitance of 1

fF/μm2 with 3.3 V of power supply headroom. In a 150 μm2 pixel, if one quarter of

the area is devoted to the storage element (∼ 5.6 pF), this capacitance and power

supply could contain nearly 3.7× 104 10 keV x-rays. Applying the same dynamic

range criteria of 1% statistics per pixel, used earlier in the Digital PAD example,

this gives only an absolute dynamic range of less than a decade. For repetitive

experiments with a well defined reference time, these limitations are not a serious

obstacle, as multiple frames may be combined to yield the necessary statistics;

however, imaging systems without these characteristics pose a serious problem.

A final consideration with Analog PADs is the effect the leakage current from

the detector diode layer has on the pixel well depth. Over the course of an integra-

tion this parasitic current fills a portion of the avaliable well depth of each pixel,

dependant on the exposure duration and the detector temperature. Given that, for

a room temperature device, the level of the leakage current can easily be equivalent

to tens of thousands of x-rays per second, it is frequently necessary to cool Analog

PADs to a point where the rate of dark current accumulation becomes negligible.

3Logarithmic and other non-linear charge storage elements have been discussed but are con-sidered too susceptible to process and array wide variations as well as radiation damage to bepractical.

55

This greatly complicates the design of the detector housing as it typically requires

either a dry gas or vacuum environment to prevent condensation, which in turn

creates problems for distributing and recording high speed, high fidelity electrical

signals to and from the detector.

3.3 Contemporary PAD Projects

As we have mentioned, development of Pixel Array Detectors began with Digital

PADs in the early 1990s, followed by Analog PADs later in that decade. As a result

of years of dedicated effort a few of these projects (Digital PADs only, to-date) have

been built into large format imagers. Of these one, the Pilatus imager developed

by Dr. Christian Broennimann’s group at the Swiss Light Source, transitioned in

October of 2006 from a publicly supported R&D project to a product available

from a private company.

A general summary of the salient traits of contemporary Analog and Digital

PAD projects is offered in table 3.1. The reader should be cautioned not to draw

conclusions that are too broad from this simple comparison of PAD detectors as

there are caveats to each of these detectors that this presentation masks; caveats

that are a direct consequence of the combination of flexibility, offered by custom

designed in-pixel signal processing electronics, and constraint, imposed by the

limited pixel area, that PAD developers are faced with. Despite this disclaimer,

some very important points are evident in this table, echoing the discussion from

sections 3.1 and 3.2. Most notable is the substantially larger maximum flux of

analog over digital PADs, along with the larger well depth and generally shorter

readout time of the digital over the analog PADs.4

4The LCLS PAD is somewhat of an exception to the general rule that analog PADs requirelong readout times because of the time they require for each digitization operation. This isbecause this particular PAD performs massively parallel digitization by incorporating a precision

56

Tab

le3.

1:E

xam

ple

sof

pro

min

ent,

wor

ldw

ide,

Pix

elA

rray

Det

ecto

rpro

ject

s.A

llx-r

ayre

fere

nce

dpar

amet

ers

assu

me

anx-r

ayen

ergy

of10

keV

.

Med

ipix

–2P

ilat

us

XPA

D3

LA

DC

ornel

l10

0×

92LC

LS

PA

DM

ethod

Dig

ital

Dig

ital

Dig

ital

Dig

ital

Anal

ogA

nal

ogP

ixel

Siz

e[μ

m2]

55×

5517

2×

172

130×

130

150×

150

150×

150

110×

110

Rea

dN

oise

[x-r

ays/

pix

el]

<1

<1

<1

<1

∼2.

60.

2/1.

3R

ead

Tim

e[m

s]3

32

0.4

∼10

3<

6W

ell-D

epth

[x-r

ays/

pix

el]

214

220

212

215

∼1.

7×

104

300/

2,25

0M

ax.

Flu

x[x

-ray

s/pix

el/s

]2×

106

<8×

106

∼10

6∼

106

1012

>1×

1015

Ref

eren

ces

[48]

[17,

71,22

][7

3,12

][3

0][8

3][7

6]

57

3.4 Mixed–Mode Pixel Array Detector

While the developments in Analog and Digital Pixel Array Detectors that have

taken place since the early 1990s are a clear step towards meeting the detector

needs of modern synchrotron science, both these approaches are marked by distinct

advantages and disadvantages for synchrotron applications. These strengths and

weaknesses are particularly evident when one considers how these detectors would

perform in a continuous time resolved experiment. As we have discussed earlier in

this chapter, Digital PADs lack the high flux performance to yield broad dynamic

range with good per-pixel statistics for short integration times (� 0.1 s). Analog

PADs, while capable of handling the high fluxes needed for time resolved imaging,

are severely limited in terms of well depth as well as, typically, limited in terms

of frame rate, with notable exceptions. Because of these considerations, neither

of these detectors is well suited for continuous imaging of dynamic systems on ms

time scales.

While this is only one example of the limitations of the PADs that have been

developed or which are under development to-date, it is a scientifically important

one. As we will discuss in more detail in section 7.5, studying the dynamics

of irreversible, time-evolving systems has become increasingly important as self

assembly on molecular and atomic scales plays a more important role in industrial

and scientific research. While x-rays offer an attractive structural probe on these

length scales, these systems present challenges for in-situ measurement on time

scales below ∼1 s. This is because their growth is often irreversible and dependent

on initial conditions that are either difficult or time-consuming to reproduce. While

novel methods for studying particular systems have been developed [77], what

ADC into every pixel. Thus, although it requires ms to digitize the signal from a single pixel,because all pixels are digitized at once this long digitization time is does not significantly increasethe readout time of the detector.

58

would substantially advance the field, as we argued in the introductory chapter, is

an imager capable of investigating these time scales.

Table 3.2: Imager specifications for the Mixed–Mode PAD. All x-ray referencedparameters assume an x-ray energy of 10 keV. The detector frame rate given hereis indicative of what is attainable from a Mixed–Mode PAD hybrid; a cameraimplementation will be limited by the rate at with the large quantity of dataproduced by the Mixed–Mode PAD can be processed and stored.

Detector Format Multi-Mosaic of PAD HybridsSingle PAD Hybrid Format (ASIC) 128×128 pixelsPixel Size 150 μm × 150 μmFraming Rate 1,000 HzReadout Time < 1 msRead Noise 0.4 x-rays/pixelWell Capacity 2.6× 107 x-rays/pixelMaximum Flux > 1.0× 108 x-rays/s/pixel

Because of this and other areas where pure Digital and Analog PADs do not

meet the needs of synchrotron science, an attempt to merge the most attractive

parts of these two detector methodologies was undertaken in the Mixed–Mode

PAD. The concept that was the genesis of this project5 was based on the observa-

tion that, for any imaging detector, there is a fundamental accuracy limit set by the

relative calibration of pixels within the device. This limit is a simple consequence

of the presence of fixed pattern noise in the detector, which will be discussed in

greater detail in section 6.5. Rarely is any commercial x-ray imager calibrated

better than 0.5% in this regard. This is typically not a problem, however, be-

cause, in most practical applications, what the x-ray scientist needs is, effectively,

a value that can be expressed in normalized scientific notation with mantissa that

extends to three or four significant figures of precision. In principle, a detector

that exhibited this response could offer a dynamic range that extended beyond

the capabilities of “fixed-precision” detectors like Digital and Analog PADs, while

5Attributable to Dr. Sol Gruner, Cornell University.

59

offering a very high readout rate. In an area of 150 μm × 150 μm, it is difficult

to see how one could implement the “floating-point-precision” circuit this concept

describes. However, a limited form of this functionality can be achieved with an ar-

chitecture that more directly draws from its Digital and Analog PAD predecessors,

where a small well depth analog integrating front end (i.e. the Analog element) is

coupled to an overflow counter (i.e. the Digital element).

While this was the origin of the Mixed–Mode PAD architecture, the merits

of this architecture extend much deeper than this description implies. As will

be explained in the presentation of the pixel design in chapter 4, this front end

architecture breaks the interdependence of frame rate, well depth, and precision

that a conventional analog imager is faced with. Consequently, the specifications

that the Mixed–Mode PAD is able to attain, summarized in table 3.2, are greater

than the sum of the Digital and Analog PAD paradigms that it mixes.

60

CHAPTER 4

MIXED–MODE PAD PIXEL DESIGN

The signal processing electronics built into each Mixed–Mode PAD pixel lie at

the heart of the capabilities of this imager. On the surface the components that

make up the Mixed–Mode PAD (e.g. integrator, comparator, switched capacitor,

counter, etc.) may seem somewhat basic. However, the degree of precision required

from these components, compounded with the fact that they must fit into an area

of 150 μm × 150 μm and they must work reliably over an array spanning 19.2 mm

× 19.2 mm, all the while performing in the demanding and harsh environment of

the synchrotron, makes this task very challenging. Consequently, the pixel included

in the final ASIC is the quite non-trivial result of a substantial development effort

involving a group of people spread between the Cornell PAD development group

and our collaborators at Area Detector Systems Corporation (ADSC).

Before delving too deeply into a discussion of the design of the Mixed–Mode

PAD pixel, it is appropriate to offer a few remarks to acknowledge the contribu-

tions of various people to the development of the final Mixed–Mode PAD ASIC.

The current Mixed–Mode PAD pixel and on-chip support electronics are the re-

sult of a design process that spanned many MOSIS submissions; from the first

16 × 16 pixel prototype, in the fall of 2003, to the final 128 × 128 pixel hybrid

imager, completed at the end of 2006. Following a standard development model of

design→ implementation→ testing→ redesign, the signal processing ASIC evolved

considerably through these submissions.

In the design phase, we can distinguish between architectural level design and

circuit level design. The former occurred during regular design meetings and re-

views that took place over the extent of the project, involving collaborators from

61

ADSC: Tom Hontz, Wayne Vernon, and Skip Augustine;1 and from Cornell: Sol

Gruner, Mark Tate, and myself.2 Design, simulation, and layout of the circuits for

this ASIC fell to Skip Augustine and myself. In this task, my focus was primarily

on developing a high-performance, low-noise pixel front end, while Skip was re-

sponsible for most of the peripheral circuitry and combining the individual circuit

layouts into the full submission layout. The boundaries between these tasks were,

however, maleable, adjusting depending on the needs of a particular stage of the

project.

The critical task of testing and verifying the results of these submissions was

divided between Wayne Vernon, assisted for much of the project by Doan Nyguen,

at ADSC and myself at Cornell. In the testing, a distinction developed after

the basic functionality of design was verified, as the ADSC group moved towards

developing a wafer level ability to verify ASIC functionality, a step necessary for

ultimate commercialization, and design of custom off-chip support electronics for

the final detector, while at Cornell the focus was placed on detailed evaluation of

the device performance. None of this work could have been accomplished without

the efforts of Matt Allin, at ADSC, who managed the initial packaging of these

devices and Tom Hontz, who coordinated the flip-chip bump bonding.

In the remainder of this chapter, we will go through the final design of the

Mixed–Mode PAD pixel, breaking it down into its individual components and dis-

cussing the subtleties associated with each. This final design changed considerably

from the initial implementation as a result of the iterative, evolutionary design

process. Consequently, although the pixel was my focus in the ASIC design, this

1Of Augustine Engineering, San Diego, CA; a VLSI circuit designer contracted by ADSC towork on the Mixed–Mode PAD project.

2Matt Renzi and Alper Ercan, former member of the Cornell Detector Development Group,also deserve recognition for their foundational work on the Mixed–Mode PAD project. Whilethis work did not directly propagate into the Mixed–Mode PAD design, it set the framework formany of the early discussion of the Mixed–Mode PAD architecture.

62

design is, in fairness, a combination of effort, ideas, and learning drawn from across

our collaboration. In the conclusion of this chapter, we will review a number of

ideas, developed over the course of this project, about how this design could be

extended to create an even more capable imager in the future.

4.1 Mixed–Mode PAD Pixel Architecture

Because of the Gruner group’s history with Analog PADs, the approach taken to

this merger of methodologies began from the integrator based front end of the

Analog PAD. From a long history with x-ray CCD detectors, within both the

Gruner groups at Cornell and our collaborators at ADSC, the fundamental inter-

dependence of frame rate, well depth, and precision present in an optimized analog

detector, discussed in the previous section, was well understood. The underlying

concept of the Mixed-Mode PAD is to break this interdependence by performing

a coarse analog-to-digital conversion in-pixel during the exposure. Rather than

digitizing and counting single photons, as done by Digital PADs, the Mixed-Mode

PAD digitizes and counts blocks of photons, typically the equivalent of 100 10 keV

x-rays, leaving a small residual charge for post exposure processing. This allows

for a precision, high-gain front end without sacrificing well depth. It also permits

high speed readout as only a relatively small, in terms of total number of x-rays,

residual analog signal remains in each pixel to be digitized in the period between

exposures.

Figure 4.1 depicts the basic pixel architecture. Over time, the details of this ar-

chitecture have changed with the evolution of the pixel, but the basic structure and

essential component operations have remained the same. The basic architecture

and operation begin with an integrator that accumulates photocurrent from the de-

tector diode (Isig). Charge accumulating on the integrator (Qint = Cint(Vpix−Voutp),

as defined in figure 4.1) causes the integrator output (Voutp) to slew towards ground.

63

−

+

−

+Vth

Vref

Removal Circuit

VHV

I sig

18-bit Counter

Digital ReadoutMux.

Charge Removal Trigger

ΔQ NΔQCharge

Voutp

Cint

Qint

Integrator

Charge RemovalController

Vpix

Vouto

Voutc

Figure 4.1: High level description of the Mixed-Mode PAD pixel architecture.

When the output voltage falls below the comparator’s threshold (Vth) the charge

removal controller is activated. This circuit sends out fixed length pulses which

cause charge (ΔQ) to be removed from the integrator and increment an in-pixel

counter (NΔQ). At the end of the exposure, residual voltage at the integrator out-

put (Vres) and the number of charge removals performed are recorded so that the

total charge accumulated (Qtot) may be reconstructed by:

Qtot = Cint

(dVeqv

dNΔQ

NΔQ + Voutp

), (4.1)

where dVeqv

dNΔQis a scaling constant that converts the number of charge removal

operations into an equivalent shift of the integrator output voltage.

The initial Cornell and ADSC Mixed-Mode design utilized a reset-to-zero ar-

chitecture wherein the integrator is reset each time the comparator triggers. This

architecture benefits from its electrical simplicity; however, it substantially compli-

cates the data analysis by introducing a signal-dependent dead time. In order for

this design to work well, it is necessary to keep the reset switch open long enough

for the front end to settle after reset. For this, a triggered fixed-length pulse gen-

erator is needed. If the signal is constant during the reset period and the reset

period is of constant duration, then the dead time correction is straightforward.

Practically, however, these assumptions are not valid: synchrotron sources have

64

a signal structure that varies depending on the bunch structure and it is difficult

to build a fixed-length pulse generator whose pulse length is repetitive over long

periods.

[ms]

Voutp

[V]

-0.4 -0.2 0 0.2 0.4

0

1

2

3

(a) Voutp

[μs]V

outo

[V]

-1.5 -1 -0.5 0

0

1

2

3

(b) Voutc

[μs]

Voutc

[V]

-1 -0.5 0 0.5

0

1

2

3

(c) Vouto

Figure 4.2: Voltage traces acquired from active nodes within the pixel (AE176submission), labeled as in figure 4.1, illustrating operation with a constant testcurrent source.

To avoid these problems, the architecture was changed to a design based on the

concept of a ΣΔ-Analog-to-Digital Converter (ΣΔ-ADC). A ΣΔ-ADC operates by

accumulating signal, typically current, in an integration stage while comparing the

accumulated signal to a set threshold. Whenever the threshold is passed, a fixed

quantity of the accumulated signal is removed. The ΣΔ operation is illustrated

using the Mixed-Mode PAD in figure 4.2, which shows the response of selected

nodes within the pixel to a constant test current source. Panel (a) depicts the

output from the integrator (Voutp). Integration begins when the pixel reset switch

is opened and Voutp begins to slew towards ground. The lowest voltage reached by

Voutp corresponds to the threshold voltage (Vth) of the comparator. As Voutp crosses

Vth the comparator output (Voutc, shown in panel (b)) briefly rises, activating the

charge removal process, then a rapidly returns to ground as the removal of charge

from the front-end integrator draws Voutp once again above Vth, as shown in figure

4.2, panel (a). Because a fixed quantity of charge (ΔQ) is removed, Voutp does not

65

necessarily return to Vref ; instead, immediately after the charge removal

Voutp ≈ Vth +ΔQ

Cint

, (4.2)

where this result is only approximate because the actual voltage will vary slightly

depending on the amount of signal acquired during the charge removal. The ability

to acquire signal during the charge removal operation is a very important difference

between the ΣΔ architecture and the reset-to-zero architecture. A reset-to-zero

pixel throws away signal during the in-situ resets, so that the designer must trade

off between this reset dead time and time allowed to settle the front-end following

the abrupt reset impulse. In a ΣΔ pixel, this interdependence is broken because

signal acquired during the charge removal operation in retained. The control signal

(Vouto) for a charge removal operation is shown in panel (c). Comparing the length

of this pulse with the scope traces for Voutp or Voutc, one can see that the full

duration of the charge removal operation is many times longer than the perceivable

disturbance from the charge removal on these scope traces. By making the amount

of signal removed first-order independent3 of the duration of the removal operation

and signal intensity, this ΣΔ approach avoids the problems discussed with the

reset-to-zero architecture.

The Mixed-Mode PAD is not the first case of a ΣΔ style ADC integrated into

the pixels of an area imager. The first known example of an imaging detector of

this type was developed at Stanford University [107] for optical applications. This

imager, however, utilizes a more canonical ΣΔ-ADC architecture than does the

Mixed–Mode PAD. In the Mixed–Mode PAD, only the total number of charge re-

moval operations are recorded, as the charge removal is an asynchronous, triggered

event. In the Stanford detector, as well as most ΣΔ-ADCs charge removal occurs

3There is still a dependence on the front end settling time and input signal intensity; however,this is greatly suppressed compared to the reset-to-zero architecture. A detailed discussion ofthis dependence can be founds in the detailed discussion of the front end circuit given in section4.2.2.

66

synchronous with a sampling clock edge; i.e., a clock edge is used to activate the

comparison operation and the results of the comparison are not stored in the pixel

but rather streamed out of the detector. While this sort of temporal information

would be very desirable in some applications, it creates practical problems for high

flux-per-pixel measurements. The maximum flux-per-pixel (Φmax) tolerable by this

design is

Φmax =1

cxq

·ΔQ · fsync, (4.3)

where cxq is the x-ray charge yield, ΔQ is the quantity of charge removed in each

charge removal operation, and fsync is the synchronous sampling frequency. The

specifications for our detector require that Φmax ≥ 108 10 keV x-rays per second.

If the analog well depth of the detector is 100 10 keV x-rays, then this implies fsync

must be at least 1 MHz. While technically feasible, distributing the required clock

across the large area of the Mixed–Mode PAD pixel array was deemed very risky

due to the potential of noise coupling into the pixel’s analog front end.

Instead, an asynchronously triggered charge removal circuit was decided upon,

wherein the comparator output acts as a trigger to the charge removal controller.

This circuit, which will be discussed in detail in section 4.2.2.3, is responsible for

controlling the frequency and duration of the charge removal operation by creating

a waveform that controls the charge removal operation and increments the in-pixel

counter.

4.2 Primary Pixel Components

The remainder of this chapter is divided into two parts. The first part reviews the

primary components of the pixel, those shown in figure 4.1. The second and final

part reviews the functions of the peripheral components of the pixel.

67

4.2.1 Pixel Integrator

The integration stage is the foremost signal processing element on the Mixed-

Mode PAD pixel. As such, its performance characteristics strongly affect the

pixel’s behavior, and, therefore, it is important to thoroughly analyze this circuit

to understand how it impacts the performance of the device as a whole. We begin

this analysis with a simple derivation of the relations underlying the operation of

the integrator.

−

+Vref

Vpix Voutp

Cint

M1

φrst

Figure 4.3: Schematic of the pixel integrator.

An integrator is a relatively simple circuit whose basic schematic is shown in

figure 4.3. It comprises an operational amplifier and a capacitor (Cint), called

the feedback capacitor, connected between the amplifier output (Voutp) and the

amplifier’s inverting input (Vpix), which is also the integration node of the pixel.

The non-inverting input of the amplifier (Vpos) is connected to a fixed reference

voltage (Vref). This configuration creates a virtual ground at the integration node,

whereby the amplifier slews its output as necessary to keep the voltage at this

node fixed at Vref . Finally, a reset switch, the pMOS transistor M1, allows for

cancellation of the charge stored on the integration capacitor (Qint) prior to each

integration.

In its quiescent configuration, Vpix = Vref andQint = Cint(Vpix−Voutp). Applying

68

a small, periodic test signal (δVpix) of angular frequency ω to the input node,

i.e. Vpix → Vpix+δVpix, one finds that the effective capacitance (Ceff) of the amplifier

boosted integration capacitor is

δVoutp = −A(ω) · δVpix

⇒ δQint = Cint(1 + A(ω)) · δVpix,

⇒ Ceff =δQint

δVpix

= Cint(1 + A(ω)), (4.4)

where A(ω) is the frequency dependent gain of the amplifier and we have assumed,

for simplicity, that Qint = 0 prior to the application of δVpix. This result shows

that the amplifier acts to boost the effective size of the integration capacitor. The

importance of this amplification arises when we consider parasitic capacitance be-

tween the integration node and ground (Cpix). This causes charge sharing between

this parasitic capacitance and integration capacitor proportional to the ratio of

the of the parasitic capacitance to the effective size of the integration capacitor.

Measurements of the Mixed–Mode PAD pixel parasitic capacitance indicate that

it is ∼ 200 fF,4 four times the nominal size of the integration capacitor. As a result

only 20% of the photocurrent will be drawn onto the integration capacitor through

charge distribution. The remaining 80% depend on the amplifier’s slewing of Voutp

to be drawn onto the integration capacitor. In this way, the performance of the

integrator strongly depends on the performance of the amplifier. This also illus-

trates the importance of using a high gain amplifier, e.g. a large A(ω) in equation

4.4.

4With this architecture, this measurement may be made easily noting that when the resetswitch open Cpix creates capacitive feedback network with Cint. The gain of the amplifier withthis network should be A = (Cpix+Cint)/Cpix. Thus, by modulating Vref and measuring resultingthe amplitude at Voutp, one can estimate Cpix for a given pixel.

69

4.2.1.1 Integrator Amplifier – Performance Specifications

The front-end amplifier is arguably the most significant active circuit in the Mixed–

Mode PAD ASIC. Because of its location at the beginning of the analog signal

processing chain, its performance strongly affects the quality of the data. The

previous section showed the importance of the amplifier gain in collecting the

full photocurrent signal. However, beyond the amplifier gain, other parameters,

such as transconductance, slew rate, and power consumption, also have significant

effects on the pixel performance. In this section, we begin by laying out the

performance specifications required of the integrator amplifier. The remainder of

the section then describes the structure of the amplifier, followed by a combination

of analytical and simulated5 performance characteristics. Finally, as the amplifier

provides a path for noise to enter into the beginning of the signal processing chain,

both from sources within the amplifier and from external sources, such as the power

supply or the control and bias lines, an analysis of these amplifier aspects is also

presented.

Table 4.1 provides a summary of the design specifications for the Mixed-Mode

PAD integrator amplifier, along with the expected performance of the amplifier as

derived from SPICE simulations and analytical calculations. The design specifica-

tions listed are based on the required performance of the detector and were chosen

conservatively to ensure design robustness over a wide range of manufacturing

variations and operating conditions.

4.2.1.2 Integrator Amplifier – Architecture and Analytical Analysis

The Mixed–Mode PAD integrator amplifier uses a folded cascode topology; the

schematic of which is shown in figure 4.4 with transistor sizing given in table 4.2.

5Unless noted otherwise circuit simulations were performed with T-Spice, by Tanner ResearchInc., using transistor models for the TSMC 0.25 μm process provided by our ASIC manufacturer.

70

Table 4.1: Summary listing of design specifications and expected performance forthe pixel front-end amplifier.

Design Parameter Min. Value Max. Value Expected Value

Differential Gain 60 [dB] — 91 [dB]Gain-bandwidth Product 20 [MHz] — 37 [MHz]Phase Margin 45◦ — 57◦

Transconductance 25 [μA/V] — 47 [μA/V]Slew Rate (@ 250 fF load) 10 [V/μs] — 20 [V/μs]Total Output Referred Noise — 850 [μV] < 750 [μV]PSRR (unity gain feedback) 40 [dB] — 90.9 [dB]PSRR (capacitive feedback) 40 [dB] — 69.1 [dB]CMRR 40 [dB] — 60.0 [dB]Power Consumption — 50 [μW] 33 [μW]

This topology has merits of simplicity, wide bandwidth, and high gain potential. It

consists of a differential input stage, transistors M1 and M2 in the schematic, which

channel current generated by the nMOS bias transistors between the input and

output stages. Current channeled into the output by the M2 branch is mirrored

by the pMOS Wilson Current Mirror to subtract from the current channeled into

the output by the M1 branch. Because there is no current amplification, current

is only redirected or mirrored, the amplifier’s transconductance (Gm) is essentially

determined by the sizing and bias of the input stage. Assuming this differential

pair is well matched, so that the transconductance of the input pair is roughly

equal (gm,M1 = gm = gm,M2), then the transconductance of the amplifier may be

approximated as

Gm ≈ gm. (4.5)

The open loop output impedance of the amplifier (Zout) is given by the parallel

combination of the output impedance (1/gds) of the nMOS bias transistor in the

output branch (M10), boosted by the effect of cascoding with transistor M8, and

71

the output impedance of the pMOS Wilson Current Mirror,

Zout =gm,M8

gds,M8 · gds,M10

∣∣∣∣∣∣ gm,M3

gds,M6 · (gds,M3 + gds,M7), (4.6)

where the double lines (||) indicate the parrallel operator; i.e., A||B = (A−1 +

B−1)−1. This yields a total DC gain (ADC) of

ADC = GmZout (4.7)

= gm ·(

gm,M8

gds,M8 · gds,M10

∣∣∣∣∣∣ gm,M3

gds,M6 · (gds,M3 + gds,M7)

). (4.8)

The open loop frequency response is expected to have a single pole transfer function

given by

H(ω) =ADC

1 + ωZoutCout

, (4.9)

where Cout is the output, load, capacitance. Solving for |H(ω)| = 1 shows us that

the unity gain frequency (i.e. the gain bandwidth product (GBW)) is determined

by

ω1 = GBW ≈ Gm

Cout

. (4.10)

The biasing network matches the current generated by the pMOS bias transistor

(M0) and each of the nMOS bias transistors (M9 and M10). Letting Iioa denote

this common bias current, then the maximum output current is expected to be

±Iioa. Based on this, the output slew rate is expected to be given by

Slew Rate =

∣∣∣∣ Iioa

Cout

∣∣∣∣ . (4.11)

Previous Analog PAD designs by the Gruner Group fabricated in the 0.25 μm

TSMC process ([83, 26]) have all utilized a mirrored cascode architecture6. How-

ever, the Mixed–Mode PAD’s need for a lower power and wide bandwidth front end

(> 10 MHz, for reasons we will discuss in section 4.2.2.2) prompted a move away

6A discussion of the mirrored cascode architecture may be found in [67].

72

Vdd

Vdd Vdd

M0

M1 M2

M3 M4

M5 M6

M7 M8

M9 M10

IBP

IBN

ICN

VposVneg

Vout

Figure 4.4: Schematic of Mixed–Mode PAD integrator amplifier. Transistor sizingand multiplicity are given in table 4.2. The bulk of transistors M1 and M2 areconnected to their common source. All other bulks are connected to the analogsupply (VDDA) or analog ground (VGNDA) as is appropriate by type. No stabilizationcapacitor is needed.

73

Table 4.2: Transistor sizing for the Mixed–Mode PAD integrator amplifier de-scribed in figure 4.4. The length unit of λ is a common VLSI scaling parameterintended to allow design to be easily migrated between different processes. For theTSMC 0.25 μm process λ = 0.12 μm.

Transistor W [λ] L [λ] W Multiplicity

M0 40 40 4M1 40 5 8M2 40 5 8M3 40 10 4M4 40 10 4M5 80 3 8M6 80 3 8M7 80 5 8M8 80 5 8M9 20 80 4M10 20 80 4

from this canonical design. While the first order performance characteristics, de-

rived above, are identical for both mirrored cascode and folded cascode amplifiers,

there are subtle differences between these architectures that allow the folded cas-

code to operate at the same bandwidth, but with improved phase margin,7 noise

performance, and device matching. To understand this performance difference,

one has to look at the effect of device sizing on conductance and capacitance at

internal nodes of the amplifier while considering the noise generation and matching

of the devices connected to these nodes.

Both the mirrored cascode and the folded cascode have internal nodes that

affect the high frequency performance of the amplifier. In the mirrored cascode,

the significant internal nodes occur at the gates of the three current mirrors. The

frequencies at which these internal nodes begin to affect the phase response of the

amplifier may be approximated by calculating the ratio of the conductance of the

7For our purposes, the phase margin is the difference, measured in degrees, between the phaseof the output signal of the amplifier and -180 deg., at the unity gain frequency of the amplifier.It is important in determining the stability of the amplifier, as insufficient phase margin can leadto instability [38].

74

node to its capacitance. Typically, the conductance of the node will be dominated

by the gm of the diode-connected mirror transistor. This transistor is also one of

the dominant noise sources in the mirrored cascode architecture. Increasing its

transconductance increases its thermal and flicker noise. It is possible to reduce

the flicker noise, to an extent, by enlarging the gate area. However, enlarging the

gate area increases the node capacitance, lowering the frequencies at which these

nodes affect the amplifier frequency response. This interdependence of device

transconductance, device noise, and node capacitance links the bandwidth, phase

margin, and noise performance of the amplifier in a way that limits the performance

attainable with the mirror cascode architecture.

δVI2

I1I3

Iout

M2M1

M3

Figure 4.5: Model circuit used to analyze the effective transconductance of thenMOS folded cascode.

The situation is notably different in the folded cascode architecture. In the

Mixed–Mode PAD amplifier design, there are four internal nodes that contribute

significantly to the high frequency pole of the amplifier. Of these, only one has

the same bandwidth, noise, and phase margin trade-offs that restrict the mirror

cascode architecture.

Two of the other significant internal nodes occur at the current branching nodes

of figure 4.4, equivalent to the branching node shown in figure 4.5, where current

75

generated by the nMOS bias transistors is split between the input and output

stages. The conductance of these nodes is dominated by the source conductance

(gs = gm + gmb) of the nMOS folded cascode transistors. These cascode devices

show only a weak dependence between their transconductance and size and the

noise they contribute to the amplifier. To see this, consider the effective transcon-

ductance of the gate of these nMOS cascodes. Using the notation shown in figure

4.5, a small test voltage (δV ) applied to the gate of transistor M2 will create a

current (δI) flowing in the channel. At the source of this transistor this current will

see a current splitter comprising the drain to source conductances of transistors

M1 (gds,1) and M3 (gds,3) and source of transistor M2 (gs,2). Hence,

ΔI1 =gds,1

gds,1 + gds,3 + gs,2

δI

≈ 0, (4.12)

ΔI2 = − gs,2

gds,1 + gds,3 + gs,2

δI

≈ −δI, (4.13)

ΔI3 =gds,3

gds,1 + gds,3 + gs,2

δI (4.14)

≈ 0, (4.15)

for gds,1 � gs,2, gds,3 � gs,2. The total change in the output current is given by

ΔIout = δI + ΔI2 ≈ 0, so the effective transconductance of the nMOS cascode is

approximately zero. This, in turn, implies that the device’s contribution to the

noise of the amplifier should be negligible. It is therefore possible to use very wide

devices to get high source conductance without the concern that this will degrade

the amplifier’s noise performance.

Widening the gate has an additional effect that improves the frequency re-

sponse of the amplifier. At the current branching nodes, the dominant capacitance

is due to the bulk-to-junction capacitance of the nMOS cascode transistor. While

76

increasing the gate width will increase the overlap capacitance it also pushes the

device towards weak inversion. In weak inversion, the source capacitance dramat-

ically drops as changes in the channel charge shift from changes in the inversion

charge to changes in the depletion charge. By operating the device in weak inver-

sion, it is thus possible to use large devices, with reduced flicker noise and improved

matching, without compromising the frequency response of the amplifier.

The final two nodes occur in the pMOS Wilson Current Mirror on the output

branch. This circuit incorporates an internal feedback loop that cancels noise

generated by the cascoding pMOS devices. Since the Wilson Mirror is a relatively

common circuit element treated in many IC design books, e.g. [38], we will not

provide a detailed analysis of it here and instead state the following results:

δIout,M3 = −(

a

1 + a

)δIN,M3

≈ −δIN,M3, (4.16)

δIout,M4 =

(a

1 + a

)δIN,M4

≈ δIN,M4, (4.17)

δIout,M5 =gds,M3

gds,M3 + gs,M5

(1

1 + a

)δIN,M5

≈ gds,M3(gds,M3 + gds,M7)(gm,M4 + gs,M6)

gm,M4gm,M6(gds,M3 + gs,M5)δIN,M5, (4.18)

δIout,M6 =gm,M4

gm,M4 + gs,M6

(1

1 + a

)δIN,M6

≈ gds,M3 + gds,M7

gm,M6

δIN,M6, (4.19)

for 1 � a, where a is the open loop gain of the Wilson current mirror,

a =gm,M4gm,M6

(gds,M3 + gds,M7)(gm,M4 + gs,M6), (4.20)

δIN,Mn is the noise current generated by transistor Mn (n = 3, 4, 5, or 6) and

δIout,Mn is the resulting change in the drain current of the respective transistor. As

77

long as the transistors remain saturated, causing the drain-to-source transconduc-

tance (gds) to be small relative to the source or gate transconductance (gs and gm

resp.), equations 4.18 and 4.19 will both be ∼ 0. Thus, it is possible to operate

the cascode transistors well into weak inversion without a noise penalty, thereby

reducing their gate capacitance and boosting their transconductance, raising the

frequency at which this node begins to degrade the performance of the amplifier.

The final significant node is connected to the gates of the load transistors in

the Wilson Current Mirror. Since this node occurs on only the non-inverting

signal path in the amplifier, its degenerative effect on the frequency performance

is mitigated by the effect of the inverting signal path. To illustrate this mitigation,

recall that the signal at the output is the sum of the signals on the inverting

and non-inverting branches. Thus, if one branch has no phase shift, but equal

amplitude, the maximum phase shift a pole on the other branch can induce in the

output to 45◦. This effect can be seen directly in the frequency response of the

Mixed–Mode PAD integrator amplifier, shown in figure 4.8. Near 1 MHz, a loss

in phase margin begins to occur that plateaus between 20 MHz and 80 MHz. The

initial phase margin loss is due to the node at the gate of the load transistors in

the Wilson Current Mirror and the plateau occurs because this node affects the

frequency performance of the circuit at much lower frequencies than nodes on the

inverting signal path.

4.2.1.3 Integrator Amplifier – Performance Characteristics

The preceeding discussion of the amplifier’s architecture offers a qualitative view of

the integrator amplifier’s design. This section aims to extend this view by offering

a quantitative description of the performance limits of the amplifier.

To begin, it is necessary to specify the operating range for the integrator am-

plifier’s external controls, i.e. bias currents and reference voltage. The amplifier is

78

designed to operate within specifications over a range of bias currents (Iioa) from

2.5 μA to 7.5 μA. The upper limit of 7.5 μA is not due to the amplifier or perfor-

mance requirements of the pixel but is rather a power constraint imposed by the

power budget of the full ASIC. At Iioa = 7.5 μA, 15 μA of current is consumed by

each pixel. As the array contains 128× 128 pixels, this per-pixel consumption re-

sults in a total current draw of ∼ 0.25 A, the upper limit budgeted for this portion

of the design. Comparatively, at the nominal operating bias of Iioa = 5 μA8 the

integrator amplifiers draw nearly 165 mA, which is still a considerable amount of

power at more than half of the average total Analog power draw of the ASIC.

The lower limit of the amplifier’s operating range is set by the transconductance

requirements of the front end as determined by the maximum flux specification.

The Mixed–Mode PAD’s maximum tolerable flux of 1× 108 10 keV x-rays/pixel/s

generates nearly 44 nA of photocurrent. For this current to be drawn onto the inte-

gration capacitor, there needs to be an equivalent current draw from the capacitor

by the integrator amplifier, requiring a constant difference between Vref and Vpix.

To prevent this difference from causing a significant systematic error, we constrain

this difference to be less than 0.2% of the total analog residual full range, i.e. 2

mV. Thus, the amplifier transconductance should be no less than 22 μA/V. We

will show shortly that this is met when Iioa > 2.5 μA.

As discussed earlier in this section, the transconductance of the amplifier will

be roughly the transconductance of the input stage. Given the sizing of the in-

put transistors, they will operate in moderate to weak inversion under most bias

conditions so that a strong inversion approximation of the transconductance will

be inaccurate. For this reason, we use operating point simulations to estimate

the amplifier’s transconductance. For a nominal operating bias of Iioa = 5 μA

TSpice small signal analysis reports that the gm of the input pair is 47 μA/V at

8All simulation results reported in this section use this biasing condition.

79

Vdm [mV]

Gm

[μA

/V]

-500 0 5000

10

20

30

40

50

60

Figure 4.6: Mixed–Mode PAD integrator amplifier transconductance as a functionof differential mode input voltage.

the quiescent operating point of the amplifier. To check this over a broader region,

a simulation was conducted where the output was held at a fixed voltage while

the differential mode input was swept. The transconductance was then computed

by differentiating the resulting Iout vs Vdm curve. The results are shown in figure

4.6, where the maximum transconductance of 47 μA/V is in agreement with the

operating point analysis expectations.

To relate this result to the operational range of the amplifier’s bias current,

we first note that the largest possible change in transconductance with bias cur-

rent occurs when the the transistors are in weak inversion. In this limit, the

transconductance is directly proportional to the bias current so that we can use

our calculation of the nominal and minimal transconductance to set a conserva-

tive limit on the minimal bias current. To do this, we observe that the ratio of

the nominal transconductance (47 μA/V) to the minimum transconductance (22

μA/V) is ∼ 2. In the weak inversion limit, this ratio is equivalent to the ratio of

the nominal bias current to the minimal bias current, telling us that the minimal

bias current will be half of the nominal bias current, i.e. 2.5 μA.

80

Vin [V]V

out[V

]0 1 2 3

0

0.5

1

1.5

2

2.5

3

Figure 4.7: DC sweep simulation of the Mixed–Mode PAD integrator amplifier. Aline of unity slope through the origin is included for reference.

Beyond the biasing conditions, the input range of the integrator amplifier is

a consideration that impacts the setting of the integrator reference (Vref). To

determine this range, we first need the common mode input range of the amplifier.

A DC sweep of the non–inverting input with the amplifier configured as a unity

gain follower is shown figure 4.7. Defining the common mode input range as the

range of voltages where the difference between the non–inverting input and the

output is less than ±1 mV then it extends from 0.55 V to 2.36 V. The integrator

reference should be near the upper end of this range to allow for the specified 1 V

output slew; however, an overshoot margin is desirable so it should not be set at

the upper limit. Because of this, the operating range for the integrator reference

is 2.1 V to 1.6 V.

Under the nominal operating conditions of Iioa = 5 μA and Vref = 2.0 V, the

open loop frequency response of the amplifier was simulated—a Bode plot of the

results is shown in figure 4.8. This data is taken from an amplifier within the

pixel to as closely as possible mimic actual loading and feedback conditions. Ac-

curate estimation of this design’s frequency response is very important, because

81

[Hz]

Gai

n[d

B]

102 104 106 108-20

0

20

40

60

80

100

[Hz]

Phas

e[d

eg.]

102 104 106 108

-150

-100

-50

0

Figure 4.8: Bode plot depicting the frequency response of the Mixed–Mode PADintegrator amplifier under its nominal, 5 μA bias, operating conditions. This figureshows that the unity gain bandwidth of the amplifier is ∼30 MHz with a phasemargin of nearly 45 deg..

82

the design strives for both wide bandwidth response and low power operation. As

a result, the design operates in a regime where the first order transfer function of

equation 4.9 is not truly applicable, because the amplifier’s bandwidth extends to

the point that parasitic poles contributed by nodes within the amplifier become

significant. To further illustrate this point, during small area (16× 16 pixels) pro-

totyping fabrications, carried out before the full array submission, oscillations on

Voutp were observed in some pixels when the reset switch (φrst) was closed, although

test structures of the amplifier alone showed that it was unity gain stable. The

cause of this instability proved to be a phase shift introduced by the RC feedback

network created by the pixel parasitic capacitance, the integration capacitor, and

the closed state resistance of the reset switch. The simulated gain and phase in-

formation is measured after the feedback network with the φrst switch closed to

include any phase margin degradation this configuration produces. Also, the Cor-

related Double Sampling (CDS) circuit (which will be discussed in section 4.3.2)

was active, i.e. pass gate and clamp switch open, for the minimal capacitive load-

ing configuration. These simulations predict a DC differential gain of 91 dB with a

unity gain frequency (gain bandwidth product) of 37.4 MHz and a corresponding

phase margin of 57◦.

4.2.1.4 Integrator Amplifier – Noise Performance

Because of the sensitivity required of the front-end, the noise performance of the

integrator amplifier must be considered carefully. To present this analysis in a clear

fashion, our discussion is divided between intrinsic sources of noise (noise generated

by the amplifier alone) and the susceptibility of the design to extrinsic sources of

noise (pick-up from fluctuations outside of the amplifier, e.g. power supply ripple).

As a point of reference, one 10 keV x-ray produces a voltage shift of roughly 9.6

mV with an RMS uncertainty of 180 μV. Requiring the signal to noise ratio to be

83

at least three, at 10 keV, means that we can tolerate a noise level of up to 3.2 mV

RMS.

[Hz]

NSD

[dB

V]

100 105 1010-250

-200

-150

-100

-50

0

(a) Differential Noise Spectral Density

[Hz]

Inte

gral

NSD

[μV

]

100 105 10100

200

400

600

800

1000

(b) Integrated Noise Spectral Density

Figure 4.9: Simulated noise power spectra for the Mixed–Mode PAD integratoramplifier. The first plot shows the differential NSD while the second shows theintegrated NSD as a function of the sample & hold bandwidth, assuming a 100second integration time.

The specifications presented in table 4.1 indicate that the total intrinsic noise

from the amplifier should be less than 850 μV. This limit arises because the de-

tector’s thermal noise, i.e. kT/C noise, is expected to have a room temperature

RMS value of 1.8 mV when observed at the output of the integrator (Voutp). An

intrinsic noise contribution 850 μV increases the noise level of the front end to ∼2.0

mV, ∼10% above the detector’s thermal noise baseline. This level was chosen to

84

Table 4.3: Thermal noise contributions from dominant amplifier noise sources.The Integrated column calculation assumes a 6 MHz bandwidth (to match thebandwidth of the sample and hold stage).

Transistor Spectral [A2/Hz] Integrated [A2]

M1, M2 5.19× 10−25 3.11× 10−18

M3, M4 4.10× 10−25 2.46× 10−18

M9, M10 4.27× 10−25 2.56× 10−18

Table 4.4: Flicker noise contributions from dominant amplifier noise sources. TheSpectral column reports the value of equation 4.25 a 1 Hz.

Transistor Spectral [A2/Hz] Integrated [A2]

M1, M2 3.64× 10−19 4.54× 10−18

M3, M4 2.27× 10−19 2.83× 10−18

M9, M10 2.67× 10−20 7.28× 10−19

provide sufficient tolerance to achieve the desired sensitivity in spite of additional

noise sources in the analog readout and digitization chain.

Typically, in amplifier design, one seeks to minimize the input referred noise

to preserve the integrity of a transmitted voltage signal. However, for the Mixed–

Mode PAD the situation differs in that the input signal is ideally a constant voltage.

Because of the input voltage is static a more appropriate noise figure of merit for

this application is the output referred noise, which is typically expressed as an

RMS voltage. To calculate this level of fluctuation, one may express the noise

contribution from each component in the amplifier as a current, propagate this

Table 4.5: Total noise contributions (RMS) from dominant amplifier noise sources.Combining these results yields a root mean square voltage noise from all amplifiersources of 600 μV.

Transistor RMS Voltage Fluctuation [μV]

M1, M2 412M3, M4 343M9, M19 270

85

current to the output assuming an ideal circuit, and then multiply by the closed

loop output impedance of the amplifier. Since the amplifier in the Mixed–Mode

PAD integrator only uses linear current gain stages, the total output referred noise

is the sum, in quadrature, of these component terms. This amplifier’s closed loop

output impedance (Zout,closed) is given by

Zout,closed =Zout,open(ω)

1 + βAopen(ω), (4.21)

where, as discussed earlier in this section, Aopen(ω) is the open loop gain of the

amplifier, Zout,open(ω) is the amplifier’s open loop output impedance, and β is the

gain of the feedback network,

1

β= 1 +

Cpix

Cint

. (4.22)

In the limit 1 � βAopen(ω) this reduces to

Zout,closed ≈ 1

βGm

=Cint + Cpix

GmCint

. (4.23)

Within the amplifier two major noise sources were considered for each transis-

tor: thermal, or white, noise whose power spectral density (PSD) is given by

∂I2n,, th

∂f=

8kT

3gm, (4.24)

and flicker, or 1/f , noise whose PSD is given by

∂I2n, fl

∂f=

Kf

CoxWLfAfgm (4.25)

≈ 4μKf

L2fAfIDS,

where the approximation is valid for transistors operating within the strong inver-

sion regime.

Table 4.5 lists estimates of the noise contribution from each transistor that

is expected to be a significant noise source. Based on these calculations, the

86

total noise contribution of the integrator amplifier is expected to be 600 μV RMS.

For comparison, figure 4.9 shows the differential and integral output noise power

simulated with TSpice. From these simulated results, the total noise contribution

of the amplifier is expected to be 650 μV RMS.

[Hz]

PSR

R[d

B]

100 102 104 106 1080

20

40

60

80

100

Figure 4.10: PSRR of Mixed–Mode PAD integrator amplifier in unity gain feedbackconfiguration, i.e. reset switch closed.

[Hz]

PSR

R[d

B]

100 102 104 106 1080

20

40

60

80

100

Figure 4.11: PSRR of Mixed–Mode PAD integrator amplifier in capacitive feedbackconfiguration, i.e. reset switch open.

In addition to the amplifier’s intrinsic noise, it is also necessary to consider

the susceptibility of the amplifier to noise from extrinsic sources, most notably

the power supply and voltage bias lines. Susceptibility to power supply pickup

87

is typically encapsulated in a design parameter called the power supply rejection

ratio (PSRR), which describes the ratio of fluctuations on the power supply to

the resulting fluctuations at a node of interest, e.g. the integrator output, in the

circuit.

To evaluate the amplifier’s susceptibility to power supply pickup, two feedback

configurations are considered: the unity gain configuration that occurs when the

φrst signal is low, representing the noise that is sampled when the reset switch is

opened; and the capacitive feedback configuration that occurs when φrst is high,

representing the noise sampled by the sample and hold at the end of the integration

(see figure 4.3). The unity gain PSRR was 90.9 dB, well above the design spec-

ification. Early simulations of versions of the folded cascode architectures, which

notably differed for the architecture shown in figure 4.4 by connection of the tran-

sistor bulk of the differential pair transistors (M1 and M2) to the analog supply

voltage (VDDA) rather than their source, in the capacitive feedback configuration

yielded the very poor PSRR of 3.87 [dB] ≈ 1.56. Although this problem was fixed

in the final design, the reason for the poor PSRR in this feedback configuration is

worth discussing, because it is not a feature of the folded cascode architecture, in

particular, but a problem endemic to any PAD using an integrator type front end.

Cint

A(t)

−

+Vref+−

δVDDA

Cpix

δVout

Cneg

Figure 4.12: Model system for analyzing the effect of capacitive coupling betweenVDDA and the inverting input of the amplifier.

The problem stems from fluctuations in the source, drain, and bulk voltages of

88

the transistor connected to the inverting input (Vneg) of the amplifier differential

pair,9 caused by fluctuations of VDDA, capacitively coupling into the inverting input

of the amplifier. To see how this parasitic coupling occurs, consider the model

system shown in figure 4.12 where we assume an amplifier with an ideal PSRR

and model the effect of fluctuation on the analog supply (δVDDA) coupling through

the gate-to-bulk capacitance (Cgb), gate-to-source capacitance (Cgs), and gate-to-

drain capacitance (Cgd) of the transistor at the inverting input of the amplifier

differential pair with a single explicit capacitor,

Cneg = Cgb,M1∂Vb,M1

∂VDDA

+ Cgs,M1∂Vs,M1

∂VDDA

+ Cgd,M1∂Vd,M1

∂VDDA

, (4.26)

between the analog supply voltage (VDDA) and the inverting input (Vneg) of the

amplifier. The impedance seen through this capacitance, looking into the circuit,

is

Zin =1

iωCneg

+

(1

iωCint(A+ 1)

∣∣∣∣∣∣ 1

iωCpix

)=

Cneg + Cpix + Cint(A+ 1)

iωCneg(Cpix + Cint(A+ 1))

≈ 1

iωCneg

, (4.27)

for Cneg � Cpix +Cint(A+1), where A is the gain of the amplifier at the frequency

ω (and i =√−1). Thus, the power supply fluctuation δVDDA will induce a current

δI ≈ iωCnegδVDDA flowing onto the inverting input of the amplifier. Based on re-

sults derived in appendix B, this coupling will induce a fluctuation in the amplifier

9Transistor M1 in figure 4.4, except that we will consider here what happens when the bulk ofthis transistor (Vb,M1) is connected to the analog supply (VDDA) rather than (Vs,M1) the transistorsource, as in this schematic.

89

output (Vout) of

δVout = − CnegA

Cpix + Cint(A+ 1)δVDDA

≈ −Cneg

Cint

δVDDA, (4.28)

⇒∣∣∣∣∂VDDA

∂Voutp

∣∣∣∣ ≈ Cint

Cneg

, (4.29)

for 1 � A and Cpix � CintA.

To compare this analysis with TSpice simulations, we first must calculate Cneg.

Since the bulk of the differential pair is connected to VDDA its voltage coupling

factor is simply

∂Vb,M1

∂VDDA

= 1. (4.30)

The voltage coupling factors between the analog supply source of transistor M1 and

the analog supply drain of transistor M1 would be difficult to derive analytically

because of their presence in the feedback loop. However, they are readily available

from TSpice simulations and found (respectively) to be

∂Vs,M1

∂VDDA

= 2.66× 10−1, (4.31)

∂Vd,M1

∂VDDA

= 3.20× 10−4. (4.32)

The capacitances Cgb, Cgs, and Cgd of transistor M1 are given by TSpice small

signal analysis to be 29.8 fF, 8.4 fF, and 8.4 fF, respectively. Combining these

results gives Cneg = 32 fF. From our earlier analysis, the PSRR will be δVDDA

δVoutp≈

Cint

Cneg= 50

32= 1.56 ≈ 3.88 [dB], which is in exceptionally good agreement with the

directly simulated PSRR.

The value of Cint and the parameters comprising Cneg are restricted by other

design considerations, so there is little to be gained trying to optimizing the design

to minimize the ratio of Cneg

Cint. A more effective way to recover the PSRR is to

remove the direct coupling between VDDA and Vneg by connecting the bulk of the

90

differential pair to the source of the differential pair. This change results in a

TSpice simulated PSRR of 69.08 [dB] = 2, 844. This change will require sacrificing

some area, since the differential pair will need a separate N-well that is protected

against the formation of parasitic field channels by a guard ring. However, given

the dramatic improvement in PSRR it is a worth-while exchange.

Plots of the simulated PSRR for the amplifier under unity gain and capacitive

feedback conditions are given in figures 4.10 and 4.11, respectively. Under both

feedback configurations, the coupling between the power supply and integrator

output is reduced to less than 0.1% for any fluctuations on time scales above 1 ms.

[Hz]

CM

RR

[dB

]

100 102 104 106 1080

20

40

60

80

100

Figure 4.13: Simulated CMRR for Mixed–Mode PAD integrator amplifier.

In addition to the power supply, there are two other classes of control voltages

that offer paths for pick-up in the integrator amplifier. These are the amplifier’s

bias control and reference voltages. Pick-up on the bias lines is not a great concern

as it will only slightly alter the operating point of the amplifier but should not

directly affect the output voltage. Fluctuations in Vref are more of a concern.

Fluctuations on the bias control voltages do not strongly couple into the am-

plifier output voltage as these fluctuations either induce equal current shifts on the

inverting and non-inverting branches of the circuit that cancel at the output, as

is the case of the nMOS current source control voltage (Vbn) and pMOS current

91

source control voltage (Vbp), or are compensated for automatically by the ampli-

fier, as is the case with the nMOS cascode bias (Vcn). The main impact of these

fluctuations is to slightly shift the operating point of the amplifier. However, as

long as the set point for the integrator leaves a reasonable tolerance for these shifts

they should not create a problem.

Fluctuations on the integrator’s reference voltage (Vref) are more problematic.

Depending on the feedback configuration, these either act as a common mode

fluctuation or are boosted by the gain of the feedback network. The first condition

arises when the amplifier is configured as a unity gain follower10 which occurs when

the integrator’s reset is active. A plot of the modeled Common Mode Rejection

Ratio (CMRR) as a function of frequency is shown in figure 4.13. The second

condition arises when the reset is not active. In this case, the integration capacitor

(Cint) forms a capacitive feedback network with the parasitic capacitance at the

pixel front end resulting in a feedback gain of ∼ 1β

=Cint+Cpix

Cint

∼= 5. To minimize

the effect for both of these feedback configurations, we low-pass filter the Vref line,

both on-chip and off.

4.2.1.5 Radiation Tolerance

As with noise performance, the tight coupling between the integrator amplifier

and the overall performance of the analog front end warrants a detailed discussion

of the effects of radiation damage on this circuit. Based on the discussion from

section 2.3.2, there are two primary ways this amplifier architecture is susceptible

to radiation damage:

• Bias current reduction due to radiation induced increase in pMOS transistor

10Technically, fluctuations on Vref within the amplifier unity gain bandwidth directly propagateto Voutp. However our off-chip ADC system uses a differential front end with the reference voltageset to Vref so that the actual quantity digitized is Vref − Voutp.

92

thresholds.

• Increased leakage currents in the nMOS devices due to radiation induced

reduction in nMOS thresholds and formation of parasitic channels.

The network that generates gate voltages for the amplifier bias transistors relies

on a current input; therefore, any shifts in transistor threshold or leakage that

are common to both pixels and bias network will be automatically accounted for.

Radiation induced shifts in bias currents only occur if there is a difference in the

total dose between the pixel and the bias network.

In many experiments, most notably High Energy Physics and space applica-

tions, it is safe to assume that chip will be uniformly irradiated so that this effect

may be neglected. However, in experiments where the radiation dose is localized to

specific portions of the chip, this assumption is not necessarily valid. Crystallogra-

phy and synchrotron radiography, two likely applications of the Mixed-Mode PAD

detector, are examples of this class of experiment. With regard to crystallography,

one cannot assume uniform irradiation because crystal diffraction patterns produce

localized spots or rings of x-ray intensity. While the location of these spots or rings

may vary from experiment to experiment, experimenters will try to optimize their

setup so that the majority of the signal is collected in the active area of the array.

This bias will result in a disparity between the total dose accumulated at pixels

in the array and the total dose accumulated by the bias network on the ASIC

periphery. In synchrotron radiography, the problem is more pronounced due to

the limited extent of the beam. As the beam footprint is typically smaller than a

single chip with minimal divergence, the illuminated regions within the array will

receive a total dose orders of magnitude higher than the bias network. As a final,

more general, point, within the operating range of energies for the Mixed-Mode

PAD the detector layer significantly attenuates the x-ray beam. The bias network,

93

though, is located at the edge of the ASIC near the wire bonding pads so that it

does not benefit from this additional protection. Thus, even schemes to distribute

the radiation more evenly across the pixel array and bias network would yield sig-

nificantly mismatched total doses. For these reasons, the amplifier design must be

robust against radiation induced shifts in its bias currents.

Reduction of the bias current is problematic because it reduces the transcon-

ductance of the input transistors as well as the current available to slew the output.

The impact of these parameters on design performance was discussed previously

in this section. The radiation induced shift is compounded by a potenital power

supply droop of up to 30 mV from the wire bonded side of the pixel array to the far,

opposite edge. Both radiation damage and power supply droop can be modeled as

an increase in the threshold of the bias transistor.11 To guard against this droop

the sizing of the bias current generating transistor was chosen so that, over the

range of operating currents the ratio gm/Ids, was as small as reasonably possible.

This ratio allows one to estimate a percent change in Ids for a given threshold shift.

Based on published radiation studies of the TSMC 0.25 μm process [58], radiation

studies performed at Cornell and reported in section 6.7, and studies of the power

supply droop, we expect that the total threshold shift will be less than 50 mV at

one megarad dose in the oxide. Assuming the bias transistor is operating in strong

inversion (which it should be to minimize gm/Ids),

gm,M0/Ids,M0 = 2

√WK ′

p

LIioa

.

Using K ′p from [94] and a 5 μA bias current one finds gm,M0/Ids,M0 ≈ 6.7 V−1 so

that a 50 mV shift would reduce the bias current by roughly 34%, to 3.3 μA.

The effect of radiation induced leakage on the nMOS bias transistors has the

potential to harm the amplifier’s slewing capabilities. If the leakage current is

11In the case of supply droop one can assume an ideal (droop less) supply and increase thetransistor threshold by the amount of the droop.

94

denoted Irad, then the maximum output current will be limited to

max(Iout) = Iioa − Irad.

The value of Irad is, unfortunately, not a simple function of accumulated radiation

dose. As reported in [58], it is also influenced by the time over which the dose is

acquired and the environment of the chip during and between exposures.

In order to push the amplifier out of slew specifications, the maximum output

current would have to be reduced to below 2.5 μA. This limit means that, starting

from the nominal operating point of 5 μA and assuming a worst case radiation

and power supply droop reduced bias current of 3.3 μA,12 then 0.8 μA of nMOS

leakage would be needed to pull the amplifier out of slew specification. Based

on the measurements reported in [58], it is unlikely that this level of damage is

attainable in the normal operating life of a hybrid.13

Arguably, if the nMOS bias devices used an enclosed layout structure, as

discussed in section 2.3.2, it would mitigate most potential leakage problems.

However, small W :L ratios, e.g. the 20:80 ratio used in the current design, are

unattainable with these devices. Increasing the W:L ratio so that Enclosed Layout

Transistor (ELT) devices could be used would degrade the frequency response, by

lowering the high frequency poles and thus compromising the phase margin, as

well as worsen the noise performance of the integrator amplifier. Because of these

considerations, linear devices are used for the bias transistors.14

12As discussed previously in this section.13The largest leakage level, at 1 MRad, reported by [58] was over an order of magnitude below

this value for a minimum sized nMOS device. As noted in [58], increasing the time over whichthe dose is incurred will significantly reduce the effect of the radiation damage as will the use oflonger device.

14More recently, our group has looked at a linear radiation hardened transistor. This devicerequires substantial extra perimeter area than a standard linear transistor, so it is not particularlygood for digital circuitry, but it is a strong candidate building long nMOS devices. Details onthis structure may be found in [26].

95

4.2.1.6 Integrator Linearity

We conclude our discussion of the amplifier by returning to its performance in

the integrator, specifically looking at the linearity of the integrator’s response to a

constant current source. The design specification calls for a 1.0 V linear operating

range for the analog residual voltage. This limit is based on the fact that we

digitize with a 10–bit ADC and would like precision at the 1 mV level. Panel (a)

of figure 4.14 shows a simulation of the integrator linearity in which a constant

current source is applied to the integration node of the circuit. Panel (b) of this

figure depicts the integrator’s deviance from the ideal linear response as a function

of the integrator’s output voltage. Two linear regions exhibiting different slopes are

evident in this plot, separated by a kink at ∼ 0.8 V. The lower region (Voutp < 0.8

V) results from the cascoded pair of transistors, M8 and M10, being driven into

their ohmic region. The resulting reduction in the output impedance leads to a

proportional decrease in the amplifier’s DC gain, in accordance with equation 4.7.

The decrease in gain changes the effective capacitance of the integrator resulting

in increased charge sharing with the pixel’s parasitic capacitance.

Time [μs]

Voutp

[V]

0 200 400 6000

0.5

1

1.5

2

2.5

(a) Integrator Output vs Signal

Voutp

[V]

Linear Deviance [mV]0 50 100

0

0.5

1

1.5

2

2.5

(b) Deviation From Linear Response

Figure 4.14: Panel (a) shows a simulation of the change in the integrator outputover time in response to a constant signal current allow with a dashed line showingthe ideal response. Panel (b) shows the deviation of the simulated response fromthe ideal response.

96

As the upper linear range (0.8 V < Voutp) spans more than 1.5 V the design

specification is easily met with this amplifier and operating conditions. Although

not anticipated, if in the future a larger linear range were to be needed, it could

be achieved by reducing the integrator amplifier bias current.

4.2.2 Quantized Charge Removal

Another critical component in the Mixed-Mode PAD analog front end is the quan-

tized charge removal circuit used to accomplish the Δ-portion of the ΣΔ-operation

discussed in section 4.1. This circuit performs the task of removing a fixed quantity

of charge from the integration node whenever sufficient charge has accumulated

to trigger a removal operation. The digital logic details of the charge removal,

specifically the trigger conditions initiating a removal operation and the details

of the controller circuit, will be discussed in section 4.2.2.3. Here, we focus the

discussion and analysis on the architecture of the analog components of the charge

removal system.

The Mixed-Mode PAD uses a switched capacitor circuit to perform the quan-

tized charge removal, as outlined in figure 4.15. Under normal circuit operation

(i.e. when a removal operation is not occurring), the charge removal control clock

(φrem) is high so that the switch SW1 is open while SW2 is closed. When a charge

removal occurs SW1 closes and SW2 opens, effectively shorting the charge removal

capacitor (Crem) to the front end. This process results in a charge cancellation

whereby a total charge (holes) of ΔQ = Crem(Vref −Vlow) that had accumulated on

the integrator cancels with the charge (electrons) supplied by the charge removal

capacitor.

97

−

+

Cint

Crem

Detector Diode

SW1SW2

φrem

Vlow

Vhigh

Vref

Voutp

VHV

Figure 4.15: Schematic of the switched capacitor quantized charge removal circuitfound in the analog front end of each pixel. This circuit performs the Δ-portionof the ΣΔ-operation discussed in section 4.1.

4.2.2.1 Analog Components: The Gory Details

While prima-facia this circuit seems very straightforward, it directly connects to

the most sensitive node in the pixel. Because of this connection, there are a number

of subtle details that need to be attended to so that it is kept from degrading

the performance of the analog front end. Foremost among these details is the

choice of the passive (Vhigh) and active (Vlow) reference voltages. These references

need to be chosen with care to ensure the stability of the design, to minimize

noise contribution and leakage onto or from the integration node, and to allow for

accurate control over the quantity of the charge removed. Secondly, certain care

needs to be taken in the design of the switches (SW1 and SW2) that remove the

charge to avoid leakage current onto the integration node.

The passive reference node (Vhigh), so called because it does not draw current

and should ideally remain at a constant voltage throughout the integration cycle,

is capable of injecting charge into the analog front end whenever SW1 is closed.

98

Generally speaking, a charge of

Q = Crem(Vhigh − Vref), (4.33)

will remain on the removal capacitor when the charge removal operation ends. If

δVref describes fluctuations of Vref around its mean and δVhigh describes the resp.

fluctuation of Vhigh then, assuming these are independent, the resulting charge

fluctuation in removed charge will be

δQ = Crem(δV 2high + δV 2

ref)12 . (4.34)

To reduce this effect, we introduce a correlation between these noise sources by

using a copy of Vref to produce Vhigh. If Vref and Vhigh are copies of the same signal

then common fluctuations cancel so that δQ ≈ 0.

The active reference node (Vlow), so called because it draws current during

portions of the integration cycle, likewise requires care in design. This node also

contributes to fluctuation in the amount of charge removed in each charge removal

cycle. When the switch SW2 opens any fluctuation in the difference of Vlow and

Vhigh will result in a fluctuation of the removed charge. As with SW1, this charge

fluctuation may be reduced by correlating fluctuations on Vlow and Vhigh. Correla-

tions can be used to effectively remove external noise sources (e.g. pick-up from the

power supply) if the reference voltages (Vlow and Vhigh) are generated with iden-

tical, on chip digital-to-analog converters (DACs). In this case, the mirror pair

of DACs, integrated onto the ASIC and driving similar loads, share both analog

control signals and the transfer functions by which fluctuations on these control

lines propagate to DAC outputs. Therefore, these common fluctuations should not

induce any fluctuation in the removed charge.

These steps, though, do not address noise sources within these circuits or the

effect of charge injected into the active node during every charge removal opera-

tion. With regard to these issues, the best recourse is to minimize the impedance

99

of these nodes through capacitive coupling, either with each other or ground. High

frequency coupling is directly facilitated by the array of charge removal capaci-

tors (Crem, presenting ∼ 8 pF of capacitance across the array) while additional

capacitance is available off-chip.

A final detail that needs to be considered with regard to this circuit is the

leakage path presented by the switches SW1 and SW2. The TSMC 0.25 μm process

used to manufacture our signal processing ASIC is primarily a digital process.

As a result, this technology uses ion implantation to lower threshold voltage of

its nMOS and pMOS devices to reduce switching times. This practice leads to

substantially higher leakage than one would expect based on the reverse diode

leakage of a minimal sized source or drain diffusion. More precisely, according

to the manufacturer’s specifications, these devices may exhibit leakage levels as

high as 1 pA, a level that would be problematic for our front end, whereas leakage

from the diffusions alone should be less than 1 fA. In addition, the long term

effect of radiation on the nMOS switch (SW1) will be to further lower the effective

threshold of the device and induce parasitic leakage paths around the edges of

transistor gate.

Two techniques are used to minimize the leakage along this path. First, the

nMOS switch uses an enclosed layout structure15 to prevent the formation of par-

asitic leakage paths around the transistor gate. Second, the leakage induced by

threshold lowering, either from ion implantation or radiation damage, may be

stopped by raising the Vlow above the bulk voltage (VGNDA). Based on arguments

outlined in [63], so long as the Vlow is set no lower than ∼ 0.5 V, leakage through

SW1 should be negligible. By extension, this same argument implies that leakage

across SW2 should also be negligible.

15See section 2.3.2 for a discussion of enclosed layout transistors.

100

4.2.2.2 A Question of Fidelity: The Pixel Virtual Ground

As discussed in section 4.2.1, the integration node of the pixel (i.e. the point where

the signal processing circuit connects to the detector diode) acts as a virtual ground

due to the pixel’s integrator. An important consideration that combines the topics

of the previous two sections is the fidelity of this virtual ground. This voltage level

needs to be maintained over a wide range of input conditions; this requirement

becomes particularly important during the charge removal operation, because we

rely on this node’s fidelity to ensure the repeatability of the quantity of charge

removed.

Traditionally, a stable virtual ground is obtained from an integrator by maxi-

mizing the integrator amplifier gain, often through the use of multistage amplifiers.

In the Mixed–Mode PAD pixel, this approach alone is not sufficient due to the con-

fluence of the limited settling time available in each charge removal operation and

the limited frequency response available from high-gain two-stage amplifiers. The

Mixed–Mode PAD design parameters require that each charge removal cycle occur

in less than 1 μs, to meet the detector’s maximum flux specification, which allows

only a fraction of this time, 50% with typical settings, for the charge removal.

Because of this timing requirement, the amplifier must have sufficient response at

high frequencies to settle the virtual ground within a half a microsecond.

The remainder of this section begins by outlining a mathematical tool to es-

timate the charge removal performance of a given amplifier architecture using

commonly available amplifier parameters, specifically the gain and frequency in-

formation contained in the amplifier’s Bode plot. Using this tool, we then present

estimates for the fraction of charge accounted for in each charge removal cycle as

a function of the duration of the charge removal.

Very generally, to calculate the change in charge across the integration capacitor

101

Cpar

Cint

A(t)

I(t) Iint(t)

I par

(t)

−

+Vref

Figure 4.16: Analog input model used to derive the current transfer function,H(ω). This model lumps the capacitance of the charge removal capacitor (Crem)into the parasitic front end capacitance (Cpar).

in response to current flowing onto or from the integration node we may begin with

a time domain description of the current (I(t)) and a network response function

(H(t)) describing the integrator’s response to a unit current impulse. The time

dependent flow of current onto or off of the integration capacitor is then given by

the convolution of these functions, H(t) ∗ I(t).A case of particular interest for our front-end architecture involves how the

front end responds during a charge removal cycle. As was noted in equation 4.33,

when a charge removal cycle ends some charge may remain on the charge removal

capacitor. This equation, however, assumes that the charge removal operation

allows enough time before the cycle ends for the integrator to re-establish its virtual

ground level. A more general form of equation 4.33 would be

Q = Crem(Vhigh − Vpix), (4.35)

where Vpix is the voltage on the integrator node. This voltage will fluctuate during

the charge removal process as the amplifier reacts to the sudden cancellation of

charge caused by switching in the charge removal capacitor. Using the convolution

102

method outlined above, it is possible to assess this response by first integrating the

area under the H(t) ∗ I(t) curve over the region of time when the charge removal

operation is active to get the total charge drawn from the integration capacitor.

Then, the charge not drawn from the integration capacitor (Qres) will cause a

deviation in Vpix of

Vpix − Vref =Qres

Cint + Cpar

, (4.36)

where Cpar is defined in figure 4.16, so that the resulting error in charge removed

(ΔQerr) will be

ΔQerr =

(Crem

Cint + Cpar

)Qres. (4.37)

To determine the time dependence of the charge removal response, we will

first present an analysis assuming that the circuit is operating in its linear range,

subsequently treating what happens when it is not. To carry out an analysis of

the linear range response a particular integrator amplifier architecture’s virtual

fidelity, we will need a few mathematical tools. To derive these, begin by defining

the boxcar windowing function,

Θτrem(t) =

⎧⎪⎪⎨⎪⎪⎩1, t ∈ [−τrem, τrem],

0, otherwise,

(4.38)

where τrem represents half the charge removal time. With this function, we can iso-

late the response of the integrator during time when a charge removal is occurring

in the pixel; i.e.,

ΔQ−Qres =

∫ ∞

−∞

dtΘτrem(t) · {H(t) ∗ I(t)}

=

∫ ∞

−∞

dtΘτrem(t)1

2π

∫ ∞

−∞

dω H(ω) · I(ω)eiωt, (4.39)

where H(ω) and I(ω) are respectively the Fourier transforms of the current transfer

function and the input current, and we have cast the problem in terms of how much

103

charge is accumulated onto the charge removal capacitor during the time the charge

removal circuit is active. We model the effect of switching in the charge removal

capacitor as an impulse current source of magnitude ΔQ = Crem(Vref − Vlow), so

that,

I(t) = ΔQδ(t). (4.40)

Fourier transforming this equation gives

I(ω) = ΔQ. (4.41)

A precise form of H(t) will be presented shortly. For our current purposes, though,

it is sufficient and more convenient to expressH(t) as its Fourier transform, written

in its polar form as,

H(ω) = a(ω)eip(ω). (4.42)

Substituting equations 4.41 and 4.42 into equation 4.39, we find that

ΔQ−Qres =

∫ ∞

−∞

dtΘτrem(t)1

2π

∫ ∞

−∞

dω a(ω)eip(ω)ΔQeiωt

=ΔQ

2π

∫ ∞

−∞

dω a(ω)eip(ω)

∫ ∞

−∞

dtΘτrem(t)eiωt

=ΔQ

2π

∫ ∞

−∞

dω a(ω)eip(ω)

∫ τrem

−τrem

dt eiωt. (4.43)

Integrating the temporal integral gives us that

ΔQ−Qres =ΔQ

2π

∫ ∞

−∞

dω a(ω)eip(ω) ·[eiωτrem

iω− e−iωτrem

iω

]=

ΔQ

π

∫ ∞

−∞

dω a(ω)eip(ω) sin(ωτrem)

ω

=ΔQ

π

∫ ∞

−∞

dω a(ω) [cos(p(ω)) + i sin(p(ω))]sin(ωτrem)

ω

=ΔQ

π

∫ ∞

−∞

dω a(ω) cos(p(ω))sin(ωτrem)

ω

+ iΔQ

π

∫ ∞

−∞

dω a(ω) sin(p(ω))sin(ωτrem)

ω. (4.44)

104

Now, recalling that the transform’s magnitude (a(ω)) will be a even function of ω

while its phase (p(ω)) will be odd, we see that the second (complex) integral is an

odd function integrated over a symmetric domain. Therefore, we may eliminate it

to get that

ΔQ−Qres =ΔQ

π

∫ ∞

−∞

dω a(ω) cos(p(ω))sin(ωτrem)

ω

=2 ·ΔQπ

∫ ∞

0

dω a(ω) cos(p(ω))sin(ωτrem)

ω, (4.45)

where the final result was reached by noting that the argument of the remaining

integral is an even function over a symmetric domain.

As for the exact form of H(t), it can be derived by observing that when a

capacitor is placed across an amplifier, as Cint is in the integrator shown in figure

4.16, the amplifier has the effect of boosting the capacitor capacitance by a factor

of 1 + A(ω). At a given frequency, the fraction of the source current accumulated

onto the charge removal capacitor is given by the divider ratio

H(ω) =Cint(A(ω) + 1)

Cpar + Cint(A(ω) + 1). (4.46)

To take this analysis further we need performance parameters, specifically fre-

quency dependent gain and phase response, for the particular amplifier we wish to

analyze. Using the Mixed–Mode PAD integrator amplifier’s open loop gain (α(ω))

and phase (φ(ω)) information, a portion of which is shown if figure 4.8, we can

compute the network response function’s gain and phase response,

a(ω) =

∣∣∣∣ Cint(α(ω)eiφ(ω) + 1)

Cpar + Cint(α(ω)eiφ(ω) + 1)

∣∣∣∣ (4.47)

p(ω) = ∠

(Cint(α(ω)eiφ(ω) + 1)

Cpar + Cint(α(ω)eiφ(ω) + 1)

), (4.48)

with Cint = 50 [fF] and Cpar ≈ 200 [fF] in the Mixed–Mode PAD pixel design.

These results were then plugged into the integrand of equation 4.45,

a(ω) cos(p(ω))sin(ωτrem)

ω, (4.49)

105

[Hz]

[ns]

100 105-5000

0

5000

10000

15000

(a) τrem = 10 μs

[Hz]

[ns]

100 105-500

0

500

1000

1500

(b) τrem = 1 μs

[Hz]

[ns]

100 105-50

0

50

100

150

(c) τrem = 100 ns

[Hz]

[ns]

100 105-5

0

5

10

15

(d) τrem = 10 ns

Figure 4.17: Examples of the current transfer function (the integrand of equation4.45) for the Mixed–Mode PAD integrator amplifier at four different τrem values.

106

to compute the current transfer function. Figure 4.17 shows examples of the current

transfer function for the Mixed–Mode PAD integrator amplifier at four different

τrem values.

τrem [sec]

Rem

oval

Effec

iency

10−8 10−6 10−40

0.2

0.4

0.6

0.8

1

Figure 4.18: Fraction of charge accumulated onto the charge removal capacitor,for a pixel operating in the linear range, during a charge removal operation ofduration trem = 2τrem using the Mixed–Mode PAD integrator amplifier. In mostcases a few additional considerations are required because the quantity of chargeremoved will, temporarily, take the pixel out of the range of linear approximation.These considerations are outlined at the end of section 4.2.2.2.

Numerically integrating these current transfer functions and multiplying by 2π

gives the fraction of charge drawn onto the integrator during the charge removal

operation. Figure 4.18 shows these results for the Mixed–Mode PAD over a range

of τrem. From it, we can see that within less than 0.2 μs (recall that τrem is defined

to be half of the charge removal time) over 99% of the impulse charge has been

accumulated and that the quantity of charge removed is very stable above this

limit.

One caveat of the proceeding analysis is that it assumes that the integrator

amplifier is operating in its linear range. However, under the expected operating

conditions, this will not be the case immediately after the charge removal cycle is

initiated. The electron charge injected by the Crem will be roughly 50 fC (1 [V] ·50 [fF]) onto a total pixel capacitance of roughly 250 fF. This should result in

107

an immediate shift in the voltage of the pixel integration node relative to the

integrator reference voltage (Vpix−Vref) of 0.2 V. Although the integrator amplifier

transconductance (Gm) is nearly 50 μA/V, the slew rate is limited by the integrator

amplifier bias current (Iioa) of 5 μA. Consequently the pixel will be slew rate limited

until it reenters the linear range of the integrator amplifier; i.e. until roughly

Gm · (Vpix − Vref) = Iioa. (4.50)

Conservatively, it will take the amplifier less than 50 ns16 to slew (Vpix−Vref) from

0.2 V to 0.1 V, after which point the fractional impulse response curve of figure 4.18

becomes applicable, now representing the time it takes to acquire a given fraction

of the charge remaining after the initial slew response. To illustrate this for the

operating conditions considered above, ∼50% of the charge will be accumulated

in the first 50 ns while the integrator slews the shift in the pixel integration node

from 0.2 V to 0.1 V. It will then take another ∼80 ns to accumulate better than

98% of the remaining charge so that over 99% of the impulse charge has been

accumulated. This is notably longer than if the integrator were to remain entirely

within its linear range, but still more than a factor of five shorter than our design

specification of 0.5 μs.

4.2.2.3 Charge Removal Controller

The primary purpose of the charge removal controller is to ensure that a consistent

quantity of charge is removed from the front end with each removal operation.

From the discussion from section 4.2.2.2, stable charge removal is possible as long

as the duration of the charge removal (τrem) is long enough to sufficiently settle

the front end. Based on the discussion at the end of section 4.2.2.2, this constraint

16If all of the amplifier current of went to the integration capacitor it would only require 5 ns,however there is other capacitive loading of the integrator output which must be considered. The50 ns limit assumes that the total capacitive loading of the integrator is less than 10 · Cint.

108

implies that the charge removal controller needs to produce a control clock (φrem)

with a duration of ∼ 0.1 μs, or longer, whenever sufficient charge has accumulated

on the integrator.

−

+

Vdd

φgate

Vth

Voutp

Vbosc

Iosc

φrem

Figure 4.19: Schematic of the charge removal control circuit.

The circuit that produces this control clock is the comparator triggered gated

oscillator shown in figure 4.19. Before explaining the details of this circuit, however,

it is worth discussing the rationale behind using an oscillator as opposed to some

form of single-pulse generator. Initial prototypes of the Mixed–Mode PAD pixel

incorporated a circuit that generated a single pulse with each comparator cross-

ing; yet, this circuit exhibits a potential lock-up condition if insufficient charge is

removed during any charge removal operation to ensure that the integrator output

is above the comparator threshold (Voutp > Vth) when the removal ends. Under

normal operation, this should never pose a problem. However, there is a novel

way of using the pixel, with the oscillator architecture, to acquire a sequence of

frames with no associated readout dead time. Specifically, the architecture of the

analog residual measurement, which will be discussed in section 4.3.2, allows one

to take a non-destructive snapshot of the state of the pixel. If charge removal is

then inhibited during digital readout, it is possible to continue the integration into

the next frame without reseting the pixel. The problem comes in when the amount

of charge accumulated during the read out exceeds twice what can be removed in

109

a single charge removal. With a single-pulse generator, this will cause the circuit

to lock-up. However, with the oscillator, one may acquire, during the readout,

nearly two full charge removals, with standard Vref and Vlow settings, or roughly

200 10 keV x-rays without degrading the pixel response—for a 1 ms readout, this

is equivalent to a flux of 2 × 105 10 keV x-ray/s. This feature is quite attractive

for high frame rate experiments that meet the flux requirements, where the time

to read out the detector is a substantial fraction exposure duration.

To explain the operation of the charge removal control circuit: during the low

phase of φrem in each cycle, charge is removed from the integrator by connection of

the charge removal capacitor to the integration node of the pixel. During the high

phase, this connection is broken and the charge removal capacitor is reconnected to

the Vlow in preparation of the next removal cycle. As mentioned earlier, the trigger

for the oscillator is provided by the comparator. Due to the delay built in to the

oscillator digital feedback loop, once the trigger initiates a charge removal cycle

the comparator has no influence on the oscillator until the full cycle is completed.

If the comparator’s input returns low or is still low when a cycle completes, then a

subsequent cycle will be initiated, continuing in this fashion until sufficient charge

has been removed from the integrator to raise Voutp above Vth. Under normal

circumstances, though, only a single cycle is needed to accomplish return the pixel

to its normal operating state.

The duration of the charge removal cycle is controlled by the oscillator bias

current (Iosc). The capacitors shown in figure 4.19 are laid out to provide a capac-

itance of 0.1 pF for an effective capacitance of 0.2 pF. The duration of the charge

removal operation is then

τrem =VDDD

2Iosc

· 0.2 [pF] , (4.51)

where VDDD denotes the digital supply voltage, so that the bias currents ranging

110

from ∼ 200 nA to ∼ 2 μA yield performance within the operating specifications

of the pixel front end. This broad range of acceptable settings gives the controller

robustness against the pixel-to-pixel variations that occur across a large array—a

result of device mismatch and power supply droop. In addition, this range helps

to protect against additional variation induced by radiation damage.

As an nMOS device is used to generate Iosc there is a potential radiation damage

concern. However, the sizing of the device (W = 0.9 μm, L = 3 μm) serves to

minimize the radiation damage effects, as discussed in section 2.3, so that along

with regular annealing, as will be discussed in section 6.7, this circuit is acceptably

robust against radiation damage. Still, in future revisions of this design, radiation

hardening through the use of the radiation hard linear transistors reported in the

Ph.D. thesis of Dr. Alper Ercan [26], formerly of the Cornell PAD research group,17

should be implemented to extend the long term reliability of the imager.

4.2.2.4 Charge Removal Conclusions

From the forgoing analysis of the Mixed–Mode PAD charge removal circuit, a

number of important conclusions may be drawn regarding its impact on the per-

formance of the Mixed–Mode PAD as an imager, particulalry in terms of its effect

on the noise in the pixel signal measurement and acquisition of signal when the

charge removal is active.

Although not presented here, a number of other charge removal architectures

(e.g. reset-to-zero charge removal and constant-current/constant-time charge re-

moval [34]) were investigated for the Mixed–Mode PAD front end. These, ulti-

mately, were rejected because of the strong coupling they introduce between the

stability of the timing circuit and the uncertainty in the charge removed. In the

17Unfortunately this layout technique is some what risky as it involves violation of MOSISand TSMC design guidelines. Consequently there was not time in the Mixed–Mode PAD projectschedule to vet a layout with this change in time to incorporate it into the large area ASIC.

111

presented switched capacitor charge removal architecture the coupling between un-

certainty in the timing diminishes as the duration of the charge removal operation

is lengthened until it ultimately becomes negligible.

In addition to robustness against timing uncertainty, the Mixed–Mode PAD

switched capacitor charge removal architecture offers the benefit that it automat-

ically compensates for uncertainty in the comparator threshold. To see why, sup-

pose that a noiseless comparator triggers a charge removal operation when the

integrator output crosses the comparator threshold voltage (Voutp < Vth). Neglect-

ing the signal accumulated during the charge removal, we have that Voutp = Vth +

Crem

Cint(Vref − Vlow) following the removal. If we then allow a fluctuation in the com-

parator threshold (δVth) such that the charge removal triggers at Voutp = Vth+δVth,

then following the removal Voutp = Vth + δVth + Crem

Cint(Vref − Vlow). In this way, the

effect of the threshold variation is retained in the analog residual voltage and may,

therefore, be removed when the analog and digital data are recombined in post

processing.

Finally, because of the switched capacitor architecture used to accomplish the

charge removal, this circuit is capable of accurate photocurrent collection while

the charge removal is in process. Consequently, this circuit operates, essentially,

without dead time during an exposure.

Due to the impact of its accuracy on the ultimate accuracy of the detector,

the charge removal circuit is one of the most important and subtly complicated

elements of the Mixed–Mode PAD pixel. The architecture we have just finished

presenting is very well matched to the Mixed–Mode PAD application because it

has a very low susceptibility to noise and minimally impacts the operation of the

rest of the front end circuity.

112

4.2.3 In-pixel Counter

The counter is one of the largest area commitments in the pixel, taking up nearly

one quarter of the total transistor area in the AE207 (fall 2006) layout. Because of

the substantial fraction of the pixel area required, a compact counter architecture

is very important. In addition, it must be possible to read out and reset the

counter rapidly to minimize the interframe deadtime. Different architectures were

investigated for this circuit, ultimately settling upon the canonical pseudorandom

counter solution. At the end of this section we will offer a brief discussion regarding

this choice.

4.2.3.1 Pseudorandom Counter

One popular architecture that accomplishes these tasks utilizes a two tap Fibonacci

mode Linear Feedback Shift Register (LFSR).18 Practically speaking this is a shift

register, as shown in figure 4.20, where two selected elements are tapped off, exclu-

sively OR’ed, and then used to generate the first data element of the shift register

for the subsequent clock pulse. When n and m (as defined in figure 4.20) are chosen

appropriately, the sequence produced by clocking this circuit will have 2m − 1 ele-

ments with a predictable sequence of states.19 This allows the number of counter

clock cycles the system has undergone to be determined from knowledge of the

final state, as long as the initial state is also known.

This circuit is an elegant application of the theory of Finite Fields and, as such,

the mathematics underlying its operation are quite interesting and complicated.

A detailed discussion of the mathematical underpinnings of this circuit is offered

18So called because the sequence of elements generated is due to a linear recurrence; that is,each element may be expressed as a linear combination elements that preceeded it in the sequence.As the famous Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, . . . ) is generated by a similar recurrenceover the integers, this register structure also bears his name.

19While the sequence of states is predictable, the resulting distribution numerical values issufficiently flat that this circuit is often used as a random number generator [47].

113

READ

1 2 3 4 n m

Shift Register (clocked)

Figure 4.20: General architecture of the linear feedback shift register based pseu-dorandom counter. Figure adapted from [47].

in appendix A. For reasons discussed in this appendix, the 18-bit pseudo random

counter used in the Mixed–Mode PAD (i.e. m = 18) is able to attain the 218 − 1

possible pseudorandom counter states if a feedback tap is placed at the 11-th bit

(i.e. n = 11).

4.2.3.2 Linear Alternatives

As mentioned, this was not the only circuit investigated for the for the in-pixel

counter. The pseudorandom counter offers the advantage that it is structurally

very simple, being simply a linear shift register with minimal feedback, and, there-

fore, requires minimal space to implement. However, this structural simplicity and

compactness comes at the price of data complexity and limited functionality. The

data complexity is a consequence of the pseudorandom series of counter states the

circuit enters into and the resulting, effectively random, pattern of bits making up

the digital data stream. Because of this high level of complexity, debugging the

digital data stream a painful exercise, not recommended for persons with a short

temper. To illustrate what is meant by limited functionality of this circuit, con-

sider replacing the pseudorandom counter with a linear counter (i.e. a structure

where the bits correspond to significance in the numerical value of the counter).

Then, if a least significant bit readout architecture is used, the time to read out the

detector could be reduced in low flux/short exposure experiments by minimizing

114

the number of pixels needing to be addressed. Alternatively, one can imagine de-

signing a counter with fewer bits than the current counter, but where the highest

order bits are regularly read off the detector as the exposure is acquired, yielding

an imager whose well depth is effectively unbounded.

Because of these disadvantages, an effort was made to develop a compact linear

counter architecture to replace this canonical design, that culminated in the shift

register element detailed in section 4.3.1.1. The unfortunate drawback of this

circuit is that, because of its very compact layout, its radiation tolerance is not

sufficient to act as a counter in a synchrotron application, as the long term effects

of radiation damage steadily activate the elements nMOS components, slowing

down transitions for the devices low to high state and ultimately pinning every

state node in the low state—until the damage is removed through annealing as

will be discussed in section 6.7. The limited radiation tolerance of this circuit is,

however, not a concern in its application in the pixel diagnostic circuit, which we

will discuss in further detail in section 4.3.1.1, as low states in this register simply

disable the diagnostic structures.

4.2.3.3 Counter Conclusions

For better radiation tolerance, the decision was ultimately made to adopt the

canonical pseudorandom counter using a common register element.20 Although this

circuit does not use a radiation hardened layout, the larger spacing of its transistors

combined with the fact that, unlike a linear ripple counter, it is externally clocked,

and therefore does not couple state changes in one element with driving state

changes in another, yields higher radiation tolerance, as evidenced by the radiation

20Each register element is a master/slave pair of D-latches operating with opposite logic. TheD-latches are simply a cross coupled inverter pair with a CMOS switch in the feedback path anda inverting buffer as an input, that is active when the feedback switch is open and inactive whenit is closed. Schematics of this circuit may be found in [7].

115

damage assessment that will be presented in section 6.7.

4.3 Periphery Pixel Components

In addition to the basic elements of the pixel already discussed, there are a number

of peripheral components whose operation supports the pixel and allows it to

interface with the external world. These include:

Pixel Diagnostic Circuit: An externally programmable circuit responsible for

routing signals nodes from within the pixel onto a diagnostic bus for external

monitoring as well as providing test inputs to the pixel.

Pixel Correlated Double Sampling: An analog noise reduction circuit, pri-

marily intended to reduce the low frequency noise of the pixel.

Pixel Sample and Hold: The final analog output and buffering stage within the

pixel.

The following sections will provide a discussion and analysis of these circuits.

Bit 0

Bit 1

Bit 2

Bit 3

Bit 4

Bit 5Con

trol

Shi

ft R

egis

ter φ0

φ1

φ2

φ3

φ4

φ5

Qcsr

Dcsr

φadv

φclr

(a) CSR

−

+Vbias

Vdiag

Voutsh

Voutc

Vouto

Voutp

φ1

φ2

φ3

φ4

φ5

φ5

φ5

(b) Analog MUX and Output Buffer

φ0

Vpix

Vbtst

Itst

Vcal

(c) Itst Source

Figure 4.21: Elements of the pixel diagnostic circuit. Panel (a) shows the shiftregister used to control the diagnostic circuit (i.e. the Control Shift Register orCSR). Panel (b) shows the analog MUX and output buffer used to drive waveformswithin the pixel to test point on the ASIC periphery. Panel (c) shows the testcurrent source connected to the integration node of each pixel.

116

4.3.1 Pixel Diagnostic Circuit

In a complicated, large-area arrayed device, such as the Mixed-Mode PAD, it is

very important to have diagnostic capabilities within each pixel. This allows char-

acterization of how the pixel performance varies with location in the array. It also

provides an invaluable tool for isolating array-level problems to specific portions

of the design. For this reason, every pixel within the Mixed–Mode PAD contains

the externally programmable diagnostic circuit shown in figure 4.21. The diagnos-

tic structure may be broken down into three components: a control shift register

used to configure the circuit’s behavior; a MUX and buffer combination to trans-

mit waveforms from critical internal nodes within the pixel to monitoring points,

probe and wire bonding pads, on the ASIC periphery; and a test current source

that allows a variable level of current to be injected onto the pixel’s integration

node.

4.3.1.1 Control Shift Register

Because of the space restrictions within the pixel and array, the space available for

diagnostic elements is limited as is the number of output lines for diagnostic mon-

itoring. To monitor multiple critical nodes within multiple pixels, it is necessary

to have a programmable multiplexing system that allows individual signals of in-

terest to be selected and driven to probe or bonding pads on the ASIC periphery.

Control of this multiplexer, as well as other aspects of the diagnostic circuit as

detailed in table 4.6, comes from a six-bit shift register included in every pixel, the

Control Shift Register (CSR). These registers are chained together in a column-

wise fashion to facilitate programming. From a functional standpoint this design

seems unremarkable. However, at the heart of this register is a unique, small-area

single-phase shift register element, modeled after a circuit developed at Caltech

117

[69].

Table 4.6: Summary of pixel diagnostic bits. Offsets are given in a big-endianformat.

CSR Bit Name Offset Function

COUNT 0 Charge Removal Control Pulse SelectCALEN 1 Diagnostic Test Source EnableOUTP 2 Integrator Output SelectOUTC 3 Comparator Output SelectOUTSH 4 Sample & Hold Output SelectAMPEN 5 Diagnostic Buffer Amplifier Enable

The fundamental register element, shown in figure 4.22, is made up of two

complementary pairs of cross–coupled inverters. Each branch of this circuit is

activated by a choke transistor (M7, M8, M11, and M12 in figure 4.22) that either

supplies its branch with or starves it of current, depending on the state of φadv.

In addition, there are two complementary sets of pass transistors (M5, M6, M9,

and M10) that provide a gate between the supplied branches and the current

starved branches, allowing the supplied branches to write their current state into

the starved branches. Because complementary sets of transistors are used it is

possible to drive this architecture using a single clock signal—whereby alternating

φadv between low and high states sequentially supplies nMOS and pMOS cross

coupled inverter stages, thus shifting data states through the register.

The risk this architecture presents is that a driven stage may overwrite the state

of the driving stage during a φadv transition. To prevent this, the pass transistors

must be made sufficiently weak relative to the choke transistors to ensure that write

back is not possible. To find conditions for reliable operation we can consider the

worst case scenario example of the transistor stack M10, M11, and M13, drawn

from panel (a) figure 4.22, under the steady state assumption that:

Vg,M10 = Vg,M11 = Vg,M13 = Vd,M10 = Vdd. (4.52)

118

Vdd

Q

Q

D

D

M1 M2 M4M3

M5 M6 M7 M8

M9 M10

M11 M12

M13 M14 M15 M16

φadv

(a) Small-Area Single-Phase Register Element: Standard Schematic

Vdd VddVdd

M1 M9 M7*

M3*

M2M5

M4*

M8*

M13 M11 M10

M15 M16

M6 M12 M14

D D

Q Q

φadv

(b) Small-Area Single-Phase Register Element: Topological Schematic

Figure 4.22: Small-area single-phase shift register element.

119

Under these circumstances, assuming that the width of all transistors is the same,

then the drain voltage of the choke transistor M11 (Vd,M11) will be roughly:

Vd,M11 ≈(

LM11 + LM13

LM10 + LM11 + LM13

)Vdd. (4.53)

Prima-facia, this result is independent of process. However, since this analysis

is intended to represent the worst case input voltage of one inverter in the cross

coupled pair, one has to consider the transition voltage of this inverter. Assuming

we have sized our nMOS and pMOS widths to balance the inverters (WPMOS ≈μe

μhWNMOS) then Vd,M11 = 0.20 · Vdd should, conservatively, yield reliable operation.

This constraint implies that LM10 = 4(LM11 + LM13) or LM10 = 8Lmin, where Lmin

is the minimal gate length allowed in the technology.

The complexity of this circuit’s description belies its true elegance. Topologi-

cally, the circuit shown in panel (a) of figure 4.22 is equivalent to that shown in

panel (b) of the same figure. In the latter figure, the transistor network has been

unraveled to show how the large number of common source/drain nodes along

with its complementary pair structure may be exploited to create a very compact

layout, with an element of this register requiring roughly 50% of the area needed

for the more traditional register architectures used elsewhere in the Mixed–Mode

PAD design.

4.3.1.2 Analog MUX and Output Buffer

The MUX and output buffer used in the diagnostic circuit both utilize relatively

standard architectures. The MUX is a series of CMOS pass gates that connect

in common to the input of the output buffer. The output buffer, in turn, is a

basic, five transistor, amplifier with a pMOS input stage, configured as a unity

gain follower.

The simplicity of this architecture has consequences that need to be mentioned.

120

Vin [V]

Vout[V

]

0 1 2 30

0.5

1

1.5

2

2.5

3

(a) Follower RangeIbuf [μA]

Gm

[μA

/V]

100 102100

101

102

(b) Transconductance

Figure 4.23: Performance characteristics of the diagnostic buffer amplifier.

With regard to the Analog MUX, when power is initially applied to the ASIC the

CSR will enter into a random state, arbitrarily opening and closing the channels

of the MUX and thereby shorting together active nodes within the pixel. If the

pixel is powered at this point, then this random CSR configuration can result in

an unacceptably high system power draw. To prevent this potentially damaging

power-up situation, a clear signal (φclr) is included in the CSR which, when active,

causes cycling φadv to clear all register elements, opening all the switches in the

analog MUX. Consequently, the Mixed–Mode PAD requires a special start-up se-

quence wherein the CSR of all pixels is cleared, the DACs are programmed to set

minimal bias currents and reference voltages,21 and then the CSR is programmed

before the operating bias currents and reference voltages are loaded into the DACs.

Finally, there are a few points that are worth mentioning regarding the limits

of the output buffer in accurately reproducing waveforms from within the pixel.

These limits affect the slew rate, bandwidth, and range of the output buffer. The

21Each ASIC contains a bank of DACs on its periphery that control bias currents and voltages.Both the reference voltages and the current mirror voltages used to set bias currents within thearray are buffered to prevent loading issues. However, as a consequence, if these DACs are zeroed,the inputs of these buffers may float leading to unpredictable behavior in the ASIC.

121

slew rate limitation comes about from the substantially larger capacitance the

output buffer has to drive (Cload), relative to capacitances within the pixel. This

load is the result of the parasitic capacitance of the diagnostic bus, estimated to

be on the order of 10 pF, in parallel with the load of the off chip probing tool. The

setup typically used for work in this thesis was a model 12C Picoprobe from GHB

Industries that presents a 0.1 pF capacitive load with 1 MΩ of shunt resistance.

With this measurement configuration and the output buffer bias current (Ibuf) at

its nominal level of 10 μA, the slew rate is limited to 1 V/μs, which is at least an

order of magnitude below slew rates on nodes within the pixel.

The effect of output loading also extends to the small-signal performance of

the amplifier. In this architecture, the frequency response of this amplifier has a

low-pass characteristic with a unity-gain bandwidth of Gm/Cload, where Gm is the

amplifier transconductance which, as with the folded cascode architecture discussed

in section 4.2.1, is determined by the transconductance of the input transistors.

Panel (b) of figure 4.23 depicts Gm simulations for the output buffer as a function

of the buffer’s bias current. With the nominal Ibuf setting of 10 μA, this analysis

then predicts a unity gain bandwidth of ∼ 10 MHz, which will result in noticeable

shaping effects on all monitored nodes except for the track and hold voltage of the

pixel sample and hold circuit (Voutsh).

A final consideration is the output range over which the buffer is capable of

following an input signal. As figure panel (a) of 4.23 depicts, the output range

of the amplifier is not rail-to-rail. This occurs because the output branch of the

circuit is also one of the differential input branches. As a result, it is possible for

the output to rise high enough to drive the pMOS bias transistor out of saturation

and into its ohmic region, thereby inhibiting the output’s ability to track the input.

122

4.3.1.3 Test Current Source

The final element of this circuit is a current source that supplies a test current (Itst)

with which the basic functionality of the pixel may be checked.22 The structure

is a simple current mirror with one small, but significant, modification. Because

it connects to the integration node of the circuit, it will introduce some leakage

onto this node. Therefore, care must be taken to keep this leakage at a minimum.

As was discussed in section 4.2.2, modern integrated circuit technologies often use

ion-implantation to effectively lower device thresholds. This processing leaves the

device in a partially on state with current levels that could be as high as 1 pA.

To avoid this problem, a negative gate to source voltage (relative to the transistor

type) is applied, to eliminate leakage from the channel, by setting the source voltage

of the current mirror (Vcal) a few tenths of a volt below the off logic state of the

source (φ0 = VDDA).

4.3.2 Mixed-Mode PAD CDS

Correlated Double Sampling (CDS) is a technique that has been used in CCDs

and other precision measurement systems to remove low frequency noise through a

time-correlated difference measurement. The Mixed-Mode PAD pixel was designed

with an analog CDS system integrated into each pixel to allow correlated double

sampling in parallel among pixels. While at first this method seems to yield the

same behavior as the serial CDS used in CCDs and most other devices utilizing this

technique, there are important differences that can have a degenerative impact on

the performance of the detector. In fact, initial tests with the Mixed–Mode PAD

yielded surprisingly poorer performance results when CDS was used in comparison

22The accuracy of this source, particularly its temporal stability, is generally not sufficient forquantitative evaluations of the pixel performance.

123

to tests where CDS was not active. The analysis of the correlated double sampling

method presented in this section is intended as an explanation for this difference.

The section begins with a brief discussion of the Mixed-Mode PAD CDS imple-

mentation and proceeds to a general analysis and discussion of the CDS transfer

function. Then, we compare CDS with the effect of performing only a single sample

at the end of the integration. This analysis is followed by a discussion of non-ideal

behavior; that is, behavior not included in the typical first-order analysis, that

can affect the CDS measurement. Finally, conclusions are drawn, based on this

analytical work, as to the limitations of analog CDS for this sort of measurement.

−

+

Cint

CCDS

Vout

φRST

φCDS

VrefVHV

Vref

Figure 4.24: Schematic of the Mixed-Mode PAD CDS implementation.

Figure 4.24 shows a schematic of the Mixed-Mode PAD CDS circuit. The

operation of this circuit is controlled by two clock signals: φrst which gates the

pixel reset; and φCDS which clamps the tracking node of the CDS capacitor to a

reference voltage. The circuit works in four stages: 1) both switches are closed

to reset the pixel and CDS; 2) the pixel reset is opened, sampling the front end

noise and injecting charge through clock feedthrough; 3) the CDS clamp switch is

opened, allowing the tracking node to follow the pixel output; and 4) at the end

of integration the voltage on the tracking node is sampled and recorded.

124

4.3.2.1 General CDS

From a signal processing standpoint, the principle underlying CDS is that of a

high-pass filter, removing low-frequency noise through a cancellation operation.

Before deriving this transfer function, it will be useful to review the particular

noise sources that CDS attempts to remove by looking at what happens during

the opening of the reset switch.

Initially, the noise at the integration node within the pixel can be approximated

as a bandwidth limited white noise source of RMS intensity:

δVpix =

√kT

C=

[4kTR · 1

2π

∫ ∞

0

dω

1 + (ωRC)2

] 12

, (4.54)

where the familiar kT/C result has been expanded to emphasize the dependence

on the effective resistance seen from the pixel integration node even though there

is a cancellation effect of R in the source and bandwidth terms. When the pixel

reset switch is closed, the effective resistance at the integration node is small,

Rint,on < 104 ohms, whereas when the reset switch is opened, the effective resistance

of this node increases by many orders of magnitude, Rint,off > 1012 ohms. Because

of this change, opening the reset switch effectively amplifies the per-unit-bandwidth

noise at the integration node but limits the noise bandwidth to lower frequencies.

Additionally, the act of opening the switch samples some of the closed-state noise

onto the pixel, the exact quantity of which depends on the waveform used to

control the reset switch, as well as injecting charge onto the integration node via

clock feedthrough. This sampled noise and injected charge can be thought of as

very low frequency contributions to the open-reset-state noise spectrum.

If these contributions are not removed and an unfiltered measurement of the

pixel output is made, then the resulting noise contribution of the integration node,

125

both thermal and clock feedthrough, will be

δVint =

√2kT

C+δQCLK

C. (4.55)

Seen from this perspective, it should be clear why a high-pass filter, like CDS, is

desirable to suppress the low-frequency noise on the integrator front end when the

reset switch is in the open state.

4.3.2.2 CDS Transfer Function

We begin with a simplified description of the CDS transfer function,

Vout(t) = Vin(t)δ(t)− Vin(t)δ(t−Δts), (4.56)

where Vout(t) is the voltage from the pixel and Δts is the time between sampling of

the reset noise and sampling of the signal. The Fourier transform of this transfer

function is

Vout(ω) = Vin(ω)(1− e−iω·Δts), (4.57)

whose norm is ∣∣∣Vout(ω)∣∣∣2 =

∣∣∣Vin(ω)∣∣∣2 (2− 2 cos(ω ·Δts)) . (4.58)

For a given input noise spectra (Nin(ω)), the spectrum after the CDS (Nout(ω))

then becomes ∣∣∣Nout(ω)∣∣∣2 =

∣∣∣Nin(ω)∣∣∣2 (2− 2 cos(ω ·Δts)) , (4.59)

for a total output noise (NCDS, rms volts) of

NCDS =

[1

2π

∫ ∞

0

∣∣∣Nout(ω)∣∣∣2 dω] 1

2

=

[1

2π

∫ ∞

0

∣∣∣Nin(ω)∣∣∣2 (2− 2 cos(ω ·Δts))

] 12

. (4.60)

126

4.3.2.3 Effect of CDS on Low-Pass-Filtered White Noise Source

To illustrate the effect of CDS, let us consider a low-pass-filtered white noise of

spectral density An and filter time τn, so that,∣∣∣Nin(ω)∣∣∣2 =

An

1 + (τnω)2. (4.61)

After CDS this spectrum becomes∣∣∣Nout(ω)∣∣∣2 =

An

1 + (τnω)2(2− 2 cos(ω ·Δts)) . (4.62)

Figure 4.25 shows this result for four different combinations of Δts and τn, illus-

trating the dramatic changes in the post CDS spectra that relative changes in these

two time constants produce.

To further extend this result, we can integrate the post CDS spectrum to find

the total output noise,

NCDS =

[1

2π

∫ ∞

0

An

1 + (τnω)2(2− 2 cos(ω ·Δts)) dω

] 12

. (4.63)

This integral may be solved analytically using residue calculus [5]. After a little

work one finds

NCDS =[2An · (1− e−

Δtsτn )

] 12, (4.64)

the result of which is plotted in figure 4.26.

An important corollary that we can draw from equation 4.64 is that the break-

even point for low-pass-filtered white noise occurs when Δts = −τn · ln(

12

). There-

fore, as long as Δts < −τn · ln(

12

), CDS will reduce the total output noise; however,

when Δts > −τn · ln(

12

), CDS will actually amplify it.

4.3.2.4 Noise Comparison without CDS

To provide a metric with which one may gauge the effectiveness of CDS, it is

useful to consider the noise of a measurement without CDS. Here, there are two

127

Normalized Frequency [f/τn]

Filte

red

NSD

[A−

1n

]

10−40

1

2

3

4

(a) τn = 1:Δts = 100

Normalized Frequency [f/τn]

Filte

red

NSD

[A−

1n

]

10−40

1

2

3

4

(b) τn = 1:Δts = 10

Normalized Frequency [f/τn]

Filte

red

NSD

[A−

1n

]

10−40

1

2

3

4

(c) τn = 1:Δts = 1

Normalized Frequency [f/τn]

Filte

red

NSD

[A−

1n

]

10−40

1

2

3

4

(d) τn = 10:Δts = 1

Figure 4.25: Post CDS-filtering of low-pass-filtered white noise spectra for differentcombinations of τn and Δts. These figures illustrate how strongly the effectivenessof CDS is influenced by the ratio of the these two time constants.

128

[τn/Δts]

Tot

alO

utp

ut

Noi

se[A−

1 2n

]

10−2 100 102 104 106

0

0.5

1

1.5

Figure 4.26: Normalized total output noise (NCDS) of a low pass filtered white noisespectrum with noise power An and filter constant τn after CDS with sampling timeΔts.

dominant noise sources to look at: the noise contributed by thermal fluctuations

on the integration node; and noise contributed by the active devices within the

integrator amplifier.

The example of a low-pass-filtered white noise spectrum illustrates how CDS

can, in the presence of some noise spectra, increase the sampled noise relative to

a single sampling. However, a single sample does not accurately represent what

happens in a pixel without CDS. When CDS is not used, the noise at the pixel

front end is still sampled twice, once when the pixel is reset and once when the

signal is read, with a white noise contribution to these measurements of√

kTCpix

in

both cases.23 This fundamental noise sets the minimal single sample total output

noise, neglecting clock feed through, at

Nsing ≥√

2 · kTCpix

, (4.65)

23In a strict sense, this statement is not true for the sample taken at the end of the integration.At this time, the integrator effectively has a capacitive feedback network formed by Cint and Cpix.

The gain of this network, relative to fluctuations of Vpix will beCpix+(1+A(ω))Cint

(1+A(ω))Cint, where A(ω)

is the frequency dependent gain of the integrator amplifier, which is expected to vary between1 and ∼ 5 based on the Mixed–Mode PAD design specifications for Cint and estimates of Cpix.However, the bandwidth of thermal fluctuations on the integration node when the reset switch

is open should be low enough that the approximationCpix+(1+A(ω))Cint

(1+A(ω))Cint≈ 1 is valid.

129

which is the uppermost limiting value of the CDS filtered total output noise as

τn/Δts → 0. Therefore, although CDS may amplify the noise it does not make it

worse than a measurement without CDS.

The noise from the integrator amplifier will be an additive contribution to the

integration node thermal noise, both with and without CDS, and, therefore, may

be treated independently. In the case of a single sampling measurement, the front-

end electronic noise is sampled twice, once when the reset switch is opened and

again when the signal is sampled. With the first sampling, though, a charge of

(Cpix +Cint)δVoutp, where δVoutp is the sampled fluctuation in the integrator output

caused by the active circuitry in the amplifier, is sampled onto the integration node

leading to a fluctuation in the integrator’s output voltage of −Cpix+Cint

CintδVoutp. The

noise spectrum will typically not change significantly with the opening of the switch

and, like CDS, the time between samples will destructively correlate the results.

Assuming the amplifier has a single-pole low-pass characteristic and following

a similar analysis to the preceeding CDS work, we find that∣∣∣Vioa,CDS(ω)∣∣∣2 =

∣∣∣Vioa(ω)∣∣∣2 (1 +

Cpix + Cint

Cint

− 2 cos(ω ·Δtint)

), (4.66)

where Vioa(ω) is the noise spectrum of the integrator amplifier and Vioa,CDS(ω) is

the spectrum of the integrator amplifier’s contribution to a measurement without

CDS. If, as with the CDS derivation, we assume a low-pass-filtered white noise

spectrum for the front-end amplifier of low frequency amplitude An and shaping

time constant τn then the total noise contribution is

NOA,sing =

[1

2π

∫ ∞

0

An

1 + (τnω)2

(1 +

Cpix + Cint

Cint

− 2 cos(ω ·Δtint)

)dω

] 12

=

[Cpix

4Cint

An + 2An · (1− e−Δtint

τn )

] 12

. (4.67)

CDS sampling of the amplifier’s output noise will yield the same result as equation

4.64, which is smaller than the above result by the termCpix

4CintAn in the square root.

130

Thus, the electronics noise from the amplifier should be increased in a measurement

without CDS relative to one using CDS.

For both of the noise sources, this analysis argues that CDS should improve

the noise performance over measurements without CDS. It also shows us that this

advantage is marginalized when τn � Δtint. In this limit, the noise of the CDS

response will approach that of a measurement without CDS, for the low-pass-

filtered white noise spectra considered.

4.3.2.5 Analog CDS Fidelity

One item that has not been considered in the preceeding analysis is the long

term fidelity of the CDS storage capacitor. In CMOS electronics, the transistors

and integrated passive components tend to deviate from their idealized models;

consequently, an effect like leakage onto or from the CDS capacitor is a concern.

While there are a number of potential sources of capacitor leakage, the fact that the

mean leakage may be treated as analogous to dark current means that only sources

prone to significant variation need to be considered. For the CDS architecture used

in the Mixed–Mode PAD, the most variable leakage current sources are photo and

thermal electrons generated within the ASIC bulk.

Here, the leakage current results from minority carriers generated in the bulk

silicon, which diffuse into the reverse biased diode region surrounding the tran-

sistor source/drain diffusions. The diffusion length for electrons in p-type silicon

is typically hundreds of microns to a few centimeters for doping concentrations

from 1015 to 1018 acceptors per cm−3 [49]. This level of diffusion is sufficient that

a substantial fraction of these minority carriers will be drawn into the transistor

source/drain border diodes with the assistance of the weak field generated between

the substrate grounding connection and the diode edge.

In the case of thermal generation, there is a strong dependence between the

131

density of minority carriers and temperature,

p ≈ n2i

ND

; n2i ∝ (kT )3e−

Eg

kT , (4.68)

⇒ p ∝ (kT )3e−Eg

kT . (4.69)

For this reason, the temperature stability of the ASIC is critical to the hold ability

of the CDS.

While thermal effects can be significant if there is not sufficient temperature

control, photo current generated in the ASIC bulk can have an even greater ef-

fect. To understand this claim, consider the process. Photons are generated by

sources, such as room lighting, which have both statistical and systematic (e.g. 60

Hz modulation) fluctuations.24 Additionally, the probability of conversion in the

silicon obeys an exponential decay governed by the mean free path (λω) of the pho-

ton. The depth of conversion influences the fractional charge yield, as conversion

deeper into the silicon will increase blooming (i.e. lateral diffusion of the result-

ing charge cloud). The variation in the source and absorption processes combine

multiplicatively to create variablity in the CDS leakage current.

4.3.2.6 Conclusions on the Mixed–Mode PAD Analog CDS

A key difference between the serial implementation of CDS in a typical CCD and

the parallel implementation in the Mixed–Mode PAD is that the CCD has much

better control over the sampling time and the time constant of the dominant

low-pass filter. The extent of the control is described in detail in [51] wherein

it is explained how CCD designers are able to tune their CDS sampling time

and low-pass-filter time constants so as to maximize the signal to noise ratio. In a

parallel CDS device like the Mixed–Mode PAD, there is little control over the CDS

24Here, we are mainly considering the effect of ambient lighting; however, the claim holds forsource lighting, optical or x-ray, as well.

132

sampling time because it is fundamentally set by the integration time. In addition,

the sampling time is necessarily much longer than the bandpass of the front-end

electronics, to permit signal acquisition. Therefore, the benefits of Analog CDS in

the Mixed–Mode PAD are primarily restricted to low-frequency noise reduction.

This conclusion, however, presumes that one has an ideal CDS system. As

discussed earlier in this section, there are environmental factors that diminish the

fidelity of the CDS circuit. These factors can be reduced by operating the chip at

colder temperatures, improving the thermal stability, eliminating excess light on

the detector, and using wells to isolate transistors connected to charge sensitive

node from current generation in the ASIC bulk. Ultimately, though, they impose

a limit on the duration of exposures beyond which using CDS will increase the

noise of the detector. For longer integrations, a different approach to correlated

double sampling is appropriate; this method, called digital CDS, will be discussed

in section 4.3.3.

4.3.3 Pixel Sample and Hold

The pixel Sample & Hold (S&H) is the final analog stage within the pixel. It

records the state of integrator and retains this state until read out and reset. This

action is necessary in order to define an exposure window, because there is no

means to decouple the integrator from the detector diode. While sampling the

state of the integrator, the sample and hold acts as a bandwidth limiting element,

reducing the noise introduced by the integrator amplifier. Finally, this circuit acts

as a buffer to drive the analog residual voltage to high power buffers at the edge

of the chip.

The circuit that accomplishes these tasks is shown in figure 4.27. It comprises

two unity-gain follower stages, one to drive the integrator’s output voltage onto the

133

−

+

−

+

φPSH φPENAnalog OuputColumn Bus

Integrator or CDSOutput

Isolation Buffer Output BufferCsh

Figure 4.27: Schematic description of the pixel sample and hold circuit.

sample and hold capacitor (Csh) while isolating the integrator from this capacitance

and the other used to drive the sample and hold voltage to buffers on the edge

of the chip. The first stage also acts as the bandwidth limiting element of the

circuit, through a combination of capacitive loading a transconductance control.

This effect is identical to the situation discussed in section 4.3.1, wherein the

unity gain follower’s bandwidth is the ratio of the buffer’s transconductance to

the capacitance of the sample and hold capacitor (Gm/Csh). The sample and

hold capacitor is designed for 1 pF of capacitance and the transconductance of

the sampling buffer is dependent on the buffer’s bias current (Icds), as depicted in

figure 4.28. With this follower’s nominal bias current setting of 2 μA the sampling

buffer should have a transconductance of ∼6 μA/V yielding a bandwidth of 6 MHz.

The second portion of the sample and hold is the output buffer responsible for

driving the sampled residual voltage to the edge of the ASIC. This amplifier and

its compatriot buffer at the chip edge determine the maximum frequency at which

the ASIC’s analog data may be read out. The architecture of the output buffer is

a simple, five-transistor, amplifier with a pMOS input stage, identical to that of

the diagnostic output buffer, discussed in section 4.3.1, whose characteristics are

depicted in figure 4.23. Because the loading conditions for this circuit are nearly

identical to that of the diagnostic output buffer, the anticipated bandwidth of the

sample and hold output buffer is also ∼ 10 MHz at the nominal bias current of

134

Vin [V]

Vout[V

]

0 1 2 30

0.5

1

1.5

2

2.5

3

(a) Follower RangeIcds [μA]

Gm

[μA

/V]

10−2 10−1 100 10110−1

100

101

(b) Transconductance

Figure 4.28: Performance characteristics of the sample and hold isolation buffer.

10 μA.

4.3.3.1 Digital CDS

An interesting use of a sample and hold circuit is as a replacement for the analog

CDS for long (> 0.1 s) low-to-moderate intensity integrations. This operation

is accomplished by using the CDS to record the integrator output immediately

after the reset switch is opened. The recorded voltage is then read out while the

exposure is being acquired. At the end of the exposure, the detector is read out

as usual; however, offline, the initial analog reading is subtracted from the final

reading.

Mathematically, this operation is the same as the analog CDS described in

section 4.3.2 with two important differences. First, the measurement is free of

the degenerative effects associated with using CDS over long integration times.

However, as the full analog readout chain must be used to make each measurement,

the noise spectral density before the CDS is expected to be larger. At the time of

this writing, digital CDS has not yet been implemented in the Mixed–Mode PAD.

135

However the method has been well studied and reported in [50].

4.4 Design Reflections

The Mixed–Mode PAD is a device with demanding performance specifications

designed for the harsh radiation environment of the modern synchrotron light

source. The flux available from modern synchrotrons enables experiments where

signal intensities of interest can vary from billions of x-rays per mm2 per second

to a fraction of an x-ray per mm2 per second. For reasons discussed at length in

chapters 1 and 3, no x-ray imager currently in use or in development is capable

of measuring this range of signal intensities, apart from the Mixed–Mode PAD.

This range is made possible by combining the the high flux tolerance of an Analog

PAD front end and the geometric well depth to circuit area relationship found

in Digital PADs. In addition, by performing the most significant portion of the

analog-to-digital conversion in-pixel and as the exposure is taken, the Mixed–

Mode PAD is capable of breaking the interdependence of well depth, precision,

and frame rate that normally limits analog imagers, to obtain a broad dynamic

range while operating at frame rates beyond the capabilities of more conventional

x-ray imagers.

Thus, within the limits of the project’s original goals, the pixel design fabricated

in the final 128×128 pixel hybrid imager rises to the design challenges this project

has presented. Hindsight, however, offers a remarkable perspective for evaluating

a design, allowing us to see that there are ways that these goals could be extended

and a more capable detector developed in the future.

Generally, when one thinks of an imager the model that comes to mind25 is

25At least to those of the author’s generation and others who preceeded the digital-camerarevolution.

136

the film camera, where light sensitive material is exposed for a period of time dur-

ing which the illumination pattern is passively recorded. Today, nearly all x-ray

imagers still follow the film-camera paradigm of passively recording an exposure

then reporting the results after the exposure has completed. However, given mod-

ern levels of circuit integration and the availability of accessible and inexpensive

reconfigurable logic devices (i.e. a Field-Programmable Gate Arrays (FPGAs)),

it is possible to go beyond this concept. The step the Mixed–Mode PAD made

from passive pixels to active pixels (i.e. introducing pixels which respond during

an exposure to the signal they detect) was a significant advance in this direction,

resulting in a dramatic increase in well depth and frame rate without significant

sacrifices in flux tolerance. Yet, the Mixed–Mode PAD was still conceived as a

device that would collect all its signal during an exposure in the pixel during and

report the results only afterwards.

What custom signal processing and accessible reconfigurable logic offer is the

opportunity to extend the concept of an active pixel to that of an active imager.

By an active imager we mean a device where an active control system operates

during the exposure to extend and improve the capabilities of the imager. To

better explain this, consider the following two simple examples.

For the first example, consider a device like the Mixed–Mode PAD, but one

where the 18-bit pseudorandom counter is replaced by a 10-bit linear counter and

a latching 11th bit that transitions high on the change of state of the 10th counter

bit. To turn this into an active imager suppose that the 11th bit of each pixel were

read out and cleared, once every millisecond. This architecture would meet or

exceed all the design specifications of the current Mixed–Mode PAD while offering

new advantages. Notable among these, three advantages of this should be evident.

First, by reducing the number of bits in the in-pixel counter, there is a savings

137

in terms of area within the pixel that could be used, for example, to implement a

more radiation hard layout. Second, the space devoted to accumulating the 11th bit

overflows in the FPGA can be extremely large so that the well depths attainable

with this design would far exceed anything that could possibly be implemented

within a pixel alone. Finally, it is possible to process the 11th bit overflow data

within the FPGA, as the exposure is being taken. This, in turn, would make it

possible to impose other end conditions on the exposure, for example requiring

acquisition of a minimum signal in some part of the image.

As a second example, consider the problem faced by the Mixed–Mode PAD, and

any other integrating device, for long exposures where a portion of the interesting

x-ray signal is very weak. Because of the combined effects of accumulating dark

current and low-frequency noise, it is very difficult to achieve single x-ray sensitivity

in this case. Now suppose that, instead of only measuring the analog voltage at

the end of the integration the sample and hold circuit was used to track it at

regular intervals during the integration, akin to its operation in the digital CDS

technique discussed in section 4.3.3.1. So long as the sampling is more frequent

than the arrival of x-rays, digital signal processing within the FPGA should make

it possible effectively count the x-rays as they arrive. This could be implemented

in the current Mixed–Mode PAD hybrid, although it was not part of the original

design intention.

Despite the room for future development, the Mixed–Mode PAD is an im-

ager capable of performing experiments presently unaccessible to any other x-ray

imager. In the remaining chapters we will demonstrate these capabilities, first pre-

senting characterization measurements of the imager performance, then concluding

with results from the first experiments with the Mixed–Mode PAD.

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CHAPTER 5

SINGLE HYBRID CAMERA

As a final step before presenting measurements taken by the Mixed–Mode PAD,

we present a discussion of the system built to exercise it. Just as it is said, “no

man is an island,”1 no hybrid is an imager. For all its complexity, the Mixed–Mode

PAD hybrid is merely the part, although a very essential one, of a larger system

whose purpose is to quantify patterns of x-rays, translating them into meaningful

data values in the form of digital images. This chapter addresses the topic of

the imager, beyond the detector hybrid, in two parts. The initial portion offers

a presentation of the systems that support the detector hybrid and allow users

to interact with it. The later portion looks in more detail at how these systems

interact with the detector hybrid by focusing our discussion on the control signals

generated by this system and the response of the hybrid.

5.1 System Breakdown and Decomposition

Our discussion up to this point has focused on the fixed portion on the Mixed–

Mode PAD, the detector hybrid. While a substantial amount of time and effort

went into designing this device, in the end it is still only a component of the imager.

A complete set of support electronics, appropriate housing, as well as control, data

acquisition, and data analysis software are also needed for a functional imager.

Beyond this, it is the quality of these support systems that ultimately determines

the performance potential the imager is capable of achieving.

Ultimately, the goal of the Mixed–Mode PAD project is to produce a large-area

detector, 2048 pixels × 2048 pixels for roughly 310 cm × 310 cm active area con-

structed from 64 single detector hybrids. The task of building a support system

1John Donne (1572–1631), Devotions Upon Emergent Occasions, Meditation XVII.

139

Figure 5.1: Photograph of the cryostat housing the Mixed–Mode PAD single hybridcamera along with the FPGA control and frame buffer used in the camera. Notshown is the electronics rack containing the data acquisition control computer.

for this detector extends far beyond the scope of this thesis and is primarily the

responsibility of our commercial collaborators at Area Detector Systems Corpora-

tion (ADSC). In contrast, the support system, here after referred to as the camera,

built at Cornell and used to generate the bulk of the material presented in this

thesis was designed for a single detector hybrid. The purpose of its construction

was explicitly to validate and characterize the performance of the these imagers;

although the experiments presented in chapter 7 prove it is capable of doing much

more.

To simplify our discussion of the single hybrid camera, we distinguish three

sub-systems:

• Camera Housing and Detector Cryostat

• Low-Noise Support Electronics

• Data Acquisition and Control

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The remainder of this section will address each of these sub-systems in turn.

(a) Camera Front, Cover Removed (b) Camera Front with Cover

(c) Camera Front, Hybrid Removed (d) Camera Back

Figure 5.2: Photographs of the Mixed–Mode PAD from different perspectives. Theplastic tubing snaking from the top of the back plate carry chilled water, left andcenter tube in panel (a); and supply the vaccuum connection, right tube in panel(a). Panel (c) exposes the thermelectric-cooled cold finger.

5.1.1 Camera Housing and Detector Cryostat

The detector hybrid is housed in a custom vacuum cryostat, as shown in figure

5.2. Built of a brass housing with an aluminium face plate and a 50 μm thick

aluminized mylar x-ray window, it maintains a roughing pump vacuum of better

141

than 20 mTorr. In this environment, the detector is typically operated at −35◦ C;

achieved by a two-stage thermoelectric that pulls heat from a copper brick (cold

finger), that is thermally connected to the detector hybrid, into the back plate

of the camera housing, which, in turn, is water cooled. A small surface heating

element may be attached to the front of the detector to prevent condensation on the

x-ray window, when needed. With the exception of the thermoelectric control and

monitoring lines, all electrical signals are passed through the camera back plate, via

custom high-speed feed throughs,2 directly to a supporting printed circuit board

attached to the back of the detector.

5.1.2 High-Speed, Low-Noise Support Electronics

One of the design goals of the Mixed–Mode PAD is a total dead time of a millisec-

ond or less. To comprehend this task, consider the quantity of data produced by

the Mixed–Mode PAD within a single frame. A single detector hybrid has 16,384

pixels, each with 18 bits of digital data and 1 analog value that needs to be digi-

tized to ±1 mV on a 1 V range. Each hybrid is divided into eight 128× 16 pixel

banks, each bank with one digital and one analog output, so that, at the bank

level, 36,864 bits and 2,048 analog values must be read out within this millisecond.

A primary challenge faced in the design of the Mixed–Mode PAD support

electronics is the dilemma of how to maintain the fidelity of the analog residual

voltage in the presence of the high-speed signals used during detector readout.

For reasons that will be explained later in section 5.2.4, the analog readout clock

and the digital readout clock are interleaved so that both data streams are drawn

off the hybrid simultaneously. This presents a potential for crosstalk between the

2These feed throughs were built from back-to-back Mictor (Matched Impedance Connectorfrom Tyco Electronics/AMP) interconnected by PCB epoxied into the back of the camera hous-ing.

142

digital and analog data if care is not taken to protect the analog voltages from

the high-speed (specified to be up to 100 MHz) transitions on the digital clock

and data lines as well as, more significantly, the resultant transients on the power

supply lines. To accomplish this a combination of minimization, isolation, and

rejection techniques are employed.

To minimize the size of power supply transients, Low-Voltage Differential Sig-

naling (LVDS) [53] is employed on all digital lines to and from the camera. While

these circuits require a slightly higher quiescent current than modern single ended

logic, as each line must constantly drive a fixed impedance, this drawback is made

up for by reduced noise during switching, as current consumed by these drivers

changes in direction rather than magnitude.

Isolation of the analog electronics is accomplished in two ways. First, the digital

control and data lines, as well as the power planes, are kept physically separated

from the analog circuits to minimize parasitic coupling. Second, as an electrical

connection between the analog and digital electronics must exist to establish a

relative potential and this potential must, in turn, be referenced to an absolute

ground, particular care is taken with the grounding network. The absolute ground

of the design is connected to the digital ground plane (VGNDD). This is done

because the digital circuit is far more robust against pick-up from this ground line.

It also requires a lower impedance ground connection to moderate the ground

bounce caused by its own switching transients. The analog electronics, on the

other hand, are designed to draw a constant level of current, a result of the reliance

on differential elements, and, thus, transients are much smaller. More important

to the analog electronics than absolute potentials is that the potential difference

between the high and low power supply lines is maintained at a constant level.

Therefore, the analog ground plane (VGNDA) is connected to the digital ground

143

plane, within the camera, by a large (10 mH) inductor. This low-pass connection

maintains the two supplies near enough to prevent accidental forward biasing of

the transistor diffusions on the hybrid while effectively isolating the analog supply

from high-frequency noise on the digital supply.

Finally, to make the analog electronics robust against transients remaining

after the aforementioned minimization and isolation steps, all measurements are

preformed differentially with a reference that should exhibit similar noise coupling.

Jumper settings within the camera electronics make it possible to select either Vlow,

Vref , or VGNDA (as defined in the pixel architecture discussion presented in chapter

4) as an ADC reference—though the last option is only offered as a failsafe mea-

sure. In the event of a transient on one of the analog supply voltages, the similar

structures generating the analog residual voltage (Voutsh, as also defined in chapter

4), Vref , and Vlow should yield closely matching induced fluctuations. Because the

digitized value is either (Voutsh − Vref) or (Voutsh − Vlow), this operation effectively

eliminates the induced noise. As a final measure, judicious care is taken in setting

the filtering constants before the ADC so as to suppress the high-frequency pick-up

while passing as much of the low-frequency signal as possible.

5.1.3 Data Acquisition and Control

The data acquisition and control system for the Mixed-Mode PAD camera was the

result of a evolutionary process beginning with the first 16 × 16 prototype ASIC

and carried on to the large-area chip. The premise underlying this evolution has

been to provide a rapid testing platform for the Mixed–Mode PAD prototypes.

Because of this, we have avoided the complicated customized electronics adapted

by our collaborators at ADSC,3 instead relying on off-the-shelf electronics wherever

3The division of labor between our collaborators at ADSC and the group at Cornell has beenthat ADSC would design the compact, high-performance support electronics for the final multi-

144

possible.

Figure 5.3: Control and data flow within the Mixed–Mode PAD Single HybridPrototype data acquisition & control system.

The data acquisition and control system for the Mixed–Mode PAD is comprises

four elements:

• A client application running on a user computer.

• A server application running on the data acquisition and control computer

that is responsible for controlling the GPIB4 hardware, pattern generation,

pattern capture, and analog-to-digital conversion hardware.

• An FPGA5 that conditions the signals generated by the pattern generator,

hybrid detector while the Cornell group would focus on rapid testing and verification of detectorprototypes.

4General Purpose Interface Bus, also commonly known as IEEE-488 and HP-IB (Hewlett-Packard Instrument Bus). A relatively slow, but simple, data and control bus predominantlyused to automate test equipment.

5Field-Programmable Gate Array: an integrated circuit composed of programmable logic,called “logic blocks,” and programmable interconnects in which custom, reconfigurable digitallogic may be implemented.

145

generates the high speed clock sequences that read out the detector, and acts

as a frame buffer for the digital data.

• The Mixed–Mode PAD Single Hybrid Prototype Camera.

This system is illustrated in the flow diagram shown in figure 5.3.

The use of a simple TCP/IP socket based protocol to exchange commands

and queries between the Mixed-Mode PAD data acquisition controller and the

user applications has proved very beneficial, as it allows a wide variety of soft-

ware tools to control the imager. In particular, standard data acquisition and

control tools, such as LabView (National Instruments–Austin, TX) and MATLAB

(MathWorks–Natick, MA) as well as more synchrotron-specific software tools, such

as Spec (Certified Scientific Software–Cambridge, MA) and ADX (Area Detector

Systems Corporation–San Diego, CA), are easily extended to control the Mixed–

Mode PAD. Most of these tools offer command line access to socket based commu-

nications allowing the interface with the Mixed–Mode PAD acquisition controller

to be accomplished through runtime scripts. Where this is not an option, a C

library is available along with an example application (camcli) to facilitate devel-

opment of the control and status connection.

The Mixed–Mode PAD acquisition control application, known as camserv, is a

multi-threaded server coded in a mixture of C and C++. When active, i.e. having

an established connection with a user client, it operates two threads: a listener,

which waits on the socket connection for requests from use client; and a monitor,

which checks and logs selected parameters within the Mixed–Mode PAD environ-

ment, e.g. power supply voltages and current, supplying alarms when these values

step too far out of range. Interactions with the Mixed–Mode PAD camera are car-

ried out using control clock pattern generation and frame-buffering/frame-capture

systems described in the subsequent sections.

146

5.1.3.1 Control Clock Pattern Generation

At the lowest level, each detector hybrid is controlled by a sequence of clock pat-

terns. Generating these clock patterns is the combined task of a pattern genera-

tion module6 and a Field-Programmable Gate Array (FPGA).7 The purpose of the

pattern generator is to provide an easy and fast means to alter the clock pattern

sequence, a task that is made possible because the test pattern generator gener-

ates patterns based on a list of test vectors loaded into the generator’s memory

before every execution cycle. This pattern is created by software tools built into

the Mixed–Mode PAD acquisition controller and, thus, very easily altered.

There are, however, practical limits to the pattern generator. The most notable

of these is the maximum rate at which it can reliably output a sequence of test

vectors. Our system shows good performance up to roughly 10 MHz. However, at

higher rates the reliability is compromised. In addition, there exists a problem with

maintaining a given output state over the periods between sequence generation

because, during the reprogramming that occurs when a new series of sequences

is loaded into the memory of the pattern generator, the pattern generator will

return to the default, null, state. Our solution to these problems is to place an

FPGA between the pattern generator and cryostat electronics to condition the

control digital signals and generate any fast clock signals. The FPGA processes

every pattern, taking a snapshot of it and then sending it on to the camera. Based

on control signals from the pattern generator the FPGA may also latch certain

states, holding them until the latch is released, or generate specific patterns such

as the high-speed clocks that read out the detector, which the pattern generator

is incapable of generating.

6Model UC.7221 (Strategic Test–Woburn, MA).7Model Virtex-4 LX25 (Xilinx–San Jose, CA).

147

5.1.3.2 Readout and Frame Buffering

The readout of the detector is divided between the analog and digital portions

of the detector data stream. The details of the readout clock sequencing will be

discussed in section 5.2.4; here, though, we will be concerned with the paths these

two data streams take from the hybrid to the control computer.

The analog data stream is comprised of a sequence of voltages derived from

the residual voltages at the integrator output (Voutp) of each pixel. From the

analog output on the detector hybrid, this voltage is initially buffered by a high-

bandwidth, unity-gain buffer located very close, physically, to the hybrid. This

buffer drives the voltage to a high-bandwidth instrumentation amplifier8 located

just before the outputs of the camera. As discussed in section 5.1.2, this device

is a key element in the noise reduction system of the off-chip analog electronics,

as it isolates the camera analog electronics from the external analog-to-digital

conversion system, bandwidth limits the analog output signal, and makes the signal

differential to eliminate common noise. The resulting voltage is driven to a high-

speed analog-to-digital converter located in a cPCI9 bus module10 on the data

acquisition computer.

This analog readout chain provides high fidelity data but suffers from rate

limitations imposed, primarily, by the slew limits of the instrumentation amplifier.

Between the internal limits of these amplifiers and the line capacitance each must

drive (∼ 3 m of coax cable) the analog readout rate is limited to ∼ 500 kHz,

setting the deadtime of the single hybrid camera at just under 5 ms. While this is

longer than the < 1 ms targeted for the final Mixed–Mode PAD camera, tests on

hybrids alone indicate that the < 1 ms readout time is achievable if the bandwidth

8Model AD524 (Analog Devices–Norwood, MA).9CompactPCI–a 3U or 6U industrial computer architecture, where modules are connected via

a PCI backplane.10Model UC.3021 (Strategic–Woburn, MA).

148

Table 5.1: Mixed–Mode PAD digital control signals. A line above a signal nameindicates that the signal is active low.

Signal Description

READ Read enable.CKA Analog readout clock.MRST Master reset.CKD Digital readout clock.CKEN Clock enable.AMPEN In-pixel output buffer enable.PRST In-pixel integrator reset.PCL CDS clamp.PSH In-pixel sample & hold.CSRIN Pixel control register data.CSRCL Pixel control register clear.CSRCK Pixel control register clock.DACIN On-chip, refrence generating DAC data.DACCL On-chip, referencegenerating DAC clear.DACLD On-chip, reference generating DAC load.DACCK On-chip, reference generating DAC clock.

of the off-chip transmission and analog-to-digital conversion circuity is sufficiently

large. To accomplish this, however, requires high-rate analog-to-digital converters

integrated into the support electronics of the camera, a task that is underway as

part of the custom control and data acquisition electronics being developed by our

commercial collaborators at ADSC.

The digital data stream is somewhat more complicated, as the pattern capture

electronics require periodic data while, for reasons that will be discussed in section

5.2.4, the digital data from the detector hybrid has interspersed pauses to allow

the interwoven analog data to be sampled and recorded. To overcome this, the

FPGA, which generates the readout clock, is configured to act as a frame buffer,

temporarily holding one frame (exposure) worth of digital data until it may be

read into the pattern capture cPCI module11 in the data acquisition computer.

11Model UC.7021 (Strategic Test–Woburn, MA).

149

5.2 Selected Control Clock Patterns

There are a total of sixteen digital control lines used to operate each Mixed–Mode

PAD hybrid, as detailed in table 5.1. In this section, we lay out, primarily for the

benefit of those who may someday need to modify this system, how these clocks

work together to control systems in the detector hybrid.

Figure 5.4: Relation between the Mixed–Mode PAD digital control signals, asdefined in table 5.1, and systems on the detector hybrid. The CKEN signal doesnot directly affect any system on the chip, but is intended to act as a gate forthe various system clocks to prevent errant cycles. On the AE207 submission,however, there is an error in the implementation of this line, and, thus, its use isnot advised.

At a very high level each hybrid may be divided into four, nominally indepen-

dent, logical systems, as illustrated by figure 5.4. The tasks carried out by these

systems involve: configuring the global environment of the hybrid; controlling the

pixel array during an exposure; configuring the in-pixel diagnostic register; and

reading out the detector. For each of these tasks, a subset of the Mixed–Mode

PAD control signals are used in a manner that will be explained.

150

Table 5.2: Summary of the elements of the Mixed–Mode PAD global environ-ment register. This register contains the settings for the 6-bit DACs that controlthe reference voltages and bias currents used throughout the pixel array as wellas additional bits that control aspects of the detector’s behavior. More detailedinformation on these register elements may be found in [7].

Element Type Description

IMAST DAC Master Bias CurrentISS1 DAC Integrator Amplifier Bias CurrentISS2 DAC Comparator Bias CurrentISS3 DAC Gated Oscillator Bias CurrentISS4 DAC Sample & Hold, Sample Stage, Bias CurrentISS5 DAC Pixel Output Bias CurrentISS6 DAC Utility Buffer Bias CurrentISS7 DAC Test Source CurrentVREF DAC Vref Voltage (typically set from 1.6 to 2.0 V)VCAL DAC Vcal Voltage (typically set from 2.3 to 2.6 V)VLOW DAC Vlow Voltage (typically set from 0.8 to 1.2 V)VTH DAC Vth Voltage (typically set from 0.6 to 1.1 V)TMAST BIT DAC Master Current TestTSLAV BIT DAC Slave Current TestCLMODE BIT CDS SelectTCRNGE BIT Test Source Current Range

DACCK ������������������������

DACCL ��������������������������������

DACLD ��������������������������������

DACIN �����������������������������

Figure 5.5: Timing for programming the on-chip bias and reference generating 6-bit DACs as well as the global control register. Data is latched on the falling edgeof the DACCK signal so that the waveform shown here would load a hypotheticalsequence of 01010 . . . 1.

151

5.2.1 Bias/Reference DACs & Global Control Register

The first logical system involves the global environment in which the Mixed–Mode

PAD pixels operate. This includes programming the bias currents and reference

voltages that control the circuit elements within each pixel as well as setting global

logic bits that affect their operation. To accomplish this, in each detector hybrid

there are a series of 6-bit Digital-to-Analog Converters (DACs) that generate the

reference voltages and bias currents used within the pixel array. Two sets of

registers program these DACs: the first is a daisy-chained shift register (with six

successive bits for each DAC element and four most significant control bits, as

organized in table 5.2) into which the DAC settings are loaded; the second is a

latching register, with one for each element of the shift register, into which the

shift register bits are loaded when the DACLD line (active low) is asserted. At

the end of the shift register, there are four additional bits, with associated latch

register elements, that provide diagnostics for the DACs and control various global

aspects of the Mixed–Mode PAD behavior, as detailed in table 5.2. Figure 5.5

offers a timing diagram that illustrates the programming of this register.

5.2.2 Pixel Exposure Control

The second logical system within the detector hybrid controls the device during

an exposure; the detailed operation of which depends on whether or not the ana-

log CDS circuit is being used, as selected by a bit in the global control register.

As figure 5.6 illustrates, the clock timing which controls exposures is relatively

straightforward, with only a few details worth mentioning. First is the slight tim-

ing difference induced by the use of the analog CDS circuit. In both panel (a)

and panel (b) of figure 5.6, the exposure duration is given by Δtexp = tfin − tbgn;

however, the transition demarking tbgn changes depending on the use of CDS. The

152

PRST �������������������

PCL �������������������

PSH �������������������

READ ��������������������

tbgn tfin

(a) Exposure with CDS

PRST �������������������

PCL ���������������������

PSH �������������������

READ ��������������������

tbgn tfin

(b) Exposure w/o CDS

Figure 5.6: Timing diagram for the control of an exposure in the cases where analogCDS is used, panel (a), and where it is not, panel (b). Note that the location oftbgn changes between these two cases.

second point involves the timing of the PSH and READ signals at the end of the

exposure. A consequence of asserting the READ signal is that the ΣΔ operation

of the pixel is inhibited, allowing the integrator output (Voutp) to slew below the

charge removal threshold (Vth) without initiating a removal. As such, it must

be asserted after the PSH causes the pixel sample and hold to start to track the

integrator or (if active) CDS output, but before the tracking ends in a sample.

5.2.3 Pixel Control Shift Register

The structure of the pixel control shift register (CSR) was already described in

section 4.3.1; here, therefore, we focus on its programming. From the standpoint

of the CSR, the array may be seen as one (row-wise) 128 element shift register

coupled to 128 (column-wise) 128× 6 + 1 bit shift registers where the first 128× 6

bits represent the CSR elements of a complete column of pixels and the 1 extra bit

is the CSR column select bit. To program the CSR, the last bit of the last register

of each column is shifted into the array, with the right-most column shifted in

153

first. After 128 cycles of the CSRCK, clock an internal clock divider on the ASIC

generates an internal load clock, causing the contents of the row-wise register to

shift into the column-wise register. This sequence repeats, bit-by-bit, until the

column-wise register is full.

CSRCK

MRST

CSRCL

CSRIN

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Figure 5.7: Timing for programming the pixel control shift register. The datashown represents a hypothetical sequence of 101 . . . 01.

5.2.4 Pixel Readout Control

The readout clock timing is by far the most delicate in the Mixed–Mode PAD,

as it involves the careful interweaving of the CKD and CKA signals to bring the

analog and digital data off the chip at high rates. To see the need for this, one

must understand a few points of the bussing and multiplexing architecture used

to convey analog and digital data from within a pixel to output buffers at the

edge of the detector hybrid. Within the array, each column contains two data bus

lines, one which carries analog and one which carries digital data. The analog

data bus feeds into a multiplexer that connects to analog line drivers at the edge

of the ASIC. The digital data bus, in turn, leads to a latching shift register that

samples one bit of data from each column whenever latched, shifting this data

154

out at high rates in the interval between latches. This architecture is designed to

provide maximal slewing and settling time for signals on the bus lines within the

array by allowing this operation to occur as other data is being read off the chip.

Despite the tight interweaving of the analog and digital data streams, the con-

trol clocks that sequence this data (CKA and CKD, resp.) are largely autonomous.

This is because, historically, the readout of the analog and digital data was com-

pletely independent. In this primordial design, the readout scheme for the digital

data utilized separate shift registers that spanned each column, funneling the data

into the, still existent, latching shift register. This architecture, however, was

deemed to be too susceptible to catastrophic failures, caused by the loss of single

shift register elements, to be acceptable—resulting in the move to the current,

bussed, architecture. As the transition was relatively straightforward to carry out

within the framework of the existing design, no effort was made to integrate the

two clock sequences, consequently leaving a mildly maddening phase space of po-

tential clock pattern sequences with hidden pitfalls that would corrupt the data of

the unwary.

In the remainder of this section, we will try to unravel these digital, and then

analog readout clocks in an intelligible manner. This process begins by describing

each independently, in terms of the signals they generate within the hybrid, then

merging our discussion to show how they can be interwoven to read off the data

reliably.

5.2.4.1 Digital Readout Clock Timing

The digital readout clock generates two derived signals within each detector hybrid,

as illustrated in figure 5.8. The first, labeled DLATCH, causes data on the digital

bus to be recorded into the latching shift register, whence it is subsequently clocked

off the hybrid with each CKD cycle. The second, labeled DIGADV causes new

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MRST

CKD

DLATCH

DIGADV

1 2 3 4 11 12 17 18 19 20

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�������������������������������������������������������

Figure 5.8: Timing controlling the readout of the Mixed–Mode PAD digital data.MRST and CKD are external signals defined in table 5.1 while the DLATCH andDIGADV signals are derived signals generated internally on each hybrid. TheDLATCH signal causes the digital data on the array bus to be latched into theoutput shift register while DIGADV shifts data from the in pixel data register ontodigital data bus of the array.

data to be placed on the digital bus by advancing the data register of each pixel

in the active row—a process that, incidentally, resets the register as a new initial

state is clocked in to replace the data that is clocked off.

5.2.4.2 Analog Readout Clock Timing

Slightly simpler than the system driven by CKD, CKA drives a single bit through

a 17-bit shift register. When present in one of 16 bits of the register, one of the

voltages on the analog bus is multiplexed to the analog line drivers and sent off-

chip to be digitized. When present in the 1 remaining bit, the row-select register

(responsible for gating the analog and digital data of a given row onto the readout

buses) is advanced.

5.2.4.3 CKD & CKA Interweaving

The first CKA falling edge following a MRST cycle advances the row-select register,

placing the analog and digital data from the first row of pixels onto the analog and

156

MRST

CKA

ROWSEL

1 2 3 17 18 19

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Figure 5.9: Timing controlling the readout of the Mixed–Mode PAD analog data aswell as the row select logic for the digital data. MRST and CKD are external signalsdefined in table 5.1 the ROWSEL signal is a derived signal generated internally oneach hybrid. The ROWSEL signal is responsible for advancing the row select shiftregister (a 128 element single-shot shift register, reset when MRST is asserted).

digital output buses of the array. Before this occurs, however, care must be taken

to prepare the state of the data registers within the pixel to prevent write back from

occurring when the digital data is first connected to the bus. This situation is the

unfortunate consequence of the omission of a buffer between these data registers

and the digital output bus. The flip-flops used in these registers are a sequence

of two identical stages, each of which may either be in a follow or drive mode.

When in the follow mode the stage takes on the state of its data inputs. With

a transition from the follow to the drive mode, the last state seen in the follow

mode is recorded by the stage and driven on its outputs. The clocks that drive

these stages are 180 deg out of phase so that when one stage is in the follow state

the other is in the drive, and vice-versa. The problem of write back occurs when

the second stage of the last element in the pixel data registers is connected to the

bus while in drive mode, as it is possible for the state of the bus to overwrite the

state recorded in this register due to its much larger capacitance. To avoid this,

the stage must be in the record mode so that the data is isolated from the bus,

and, hence, the DIGADV-derived clock must be low.

Figure 5.10 illustrates how the data readout clocks are sequenced in the single

157

MRST

CKD

CKA

ANAREC

1 2 17 18 19

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�����������������������������������������������������������������������

Figure 5.10: Combined readout clock sequencing used in the single hybrid cam-era. In this diagram, the CKD signal is not shown at full resolution due to spacelimitations. Instead, in its first active region, there are two cycles, and, in eachsubsequent region, there are sixteen cycles (denoted by the high/low logic region).The ANAREC signal denotes the sampling clock used by the ADCs to time record-ing of the analog data. Because of the internal structure of the ADCs it must beperiodic, resulting in two redundant samples for every 16 pixels worth of analogdata. The first valid digital data comes off the chip in period 2.

hybrid camera. An additional signal (ANAREC) is included on this diagram to

indicate the timing of the sampling clock for the ADC.12 This sequencing is con-

trived to offer as much settling time as possible on the various data lines while still

being relatively straightforward to implement within the FPGA.

12Although it is not evident from figure 5.10, the ANAREC falling (sampling) edge preceedsthe activity on the CKD lines by a brief period, smaller than the resolution of the timing diagram.

158

CHAPTER 6

DETECTOR CHARACTERIZATION

A prerequisite to conducting experiments with the Mixed–Mode PAD is suffi-

cient understanding of the response of the imager to allow confident interpretation

of the images it produces. In general, an imaging device will introduce artifacts into

the raw images it produces. In a pixelated device like the Mixed–Mode PAD, these

result from a combination pixel-level effects, such as nonlinearities in the response

and electronic noise, pixelation effects, which strongly influence the imager’s spa-

tial response, and pixel-to-pixel variations. An imager needs to be characterized

with regards to these artifacts and, where necessary, calibration and correction

procedures developed to remove these effects via post acquisition processing.

This chapter deals with these characterizations, identifying primary factors con-

tributing to uncertainty in measurements made with the instruments and present-

ing baseline measurements of imager performance. Following this characterization,

the degree to which this performance meets what would be expected from an ideal

imager is evaluated through a metric called the detector quantum efficiency, which

will be defined in section 6.5. Based on this assessment, areas in which calibration

and correction could improve image quality are identified, followed by a discus-

sion of procedures to achieve this. As we will see, for a complicated device like

the Mixed–Mode PAD, the intricacies of characterization and calibration is one of

the chief obstacles to achieving the performance limits of the detector. Finally, as

this device is intended for use in an intense radiation environment, its tolerance to

radiation damage is assessed.

159

6.1 Linearity

Though linearity is often assumed by detector users, it should not be by instrumen-

tation developers. Demonstrating the linearity of an imager is therefore an essential

first step in assessing the performance of an imager. For the Mixed–Mode PAD,

this assessment in nontrivial due, on the one hand, to the fundamental nonlinearity

of the device,1 and, on the other, to the large well depth of the each pixel, which

spans from 1 to more than 25 million 10 keV x-rays, for which there is no practical

means of performing an end-to-end linearity assessment. Fortunately, these issues

may be addressed simultaneously by demonstrating the limited linearity of the

digital and analog components of the Mixed–Mode PAD data stream separately,

and, then showing that there exists a scaling factor which allows these separate

portions of the data stream to be smoothly combined into a response that is linear

over its full domain. In this way, we may satisfy ourselves that the system is indeed

linear over its entire range.

The digital portion of the linearity assessment was conducted by our collab-

orators at ADSC. It involved injecting a known test current onto the pixel inte-

gration node via a needle probe connection to the bump bonding pad of a pixel

on an un-hybridized ASIC. While this was occurring, a portion of the pixel di-

agnostic monitoring system was used to track this pixel’s analog residual voltage

(Voutp), recording the resulting rate of charge removal operations. The test cur-

rent was sourced and measured by an HP4145 Semiconductor Parameter Analyzer

and spanned a range from 1 pA to 100 nA. The charge removal frequency was

measured by a Fluke 45 Multimeter. A large resistance (∼10 MΩ) was placed in

series with the needle probe to decouple the capacitive portion of the load pre-

1Only taken together and with appropriate calibration factors do the analog and digital datastreams from the Mixed–Mode PAD form a linear data set. Independently, both data streamsare decidedly nonlinear due to the effect of the charge removal operation.

160

sented by the current source from the input to the front-end amplifier. Figure 6.1

shows the results of this measurement. At current levels below 20 pA the data

appear to notably depart from the fitted linear response. The actual magnitude

of this deviation is much smaller than the figure suggests, with its appearance

enhanced as a result of the log-log scale, and is at a level that is consistent with

the variation present in other portions of the data. Generally, a low-signal non-

linearity is unlikely to be due to the Mixed–Mode PAD as the ΣΔ front-end within

each pixel is a charge sensitive, rather than current sensitive, architecture. As a

result, any deviance from a linear response would be much more likely under high-

signal condition. As a verification of these arguments, later in this section we will

present another, independent, measurement that tests the low-signal linearity of

the Mixed-Mode PAD response.

Rat

eof

Char

geR

emov

al[H

z]

Injected Current [pA]100 101 102 103 104 105

100

102

104

106

Figure 6.1: Linearity of the digital portion of the Mixed–Mode PAD data stream,shown as the rate of charge removals as a function of stimulating current. Thismeasurement was made by sourcing a known current onto the pixel integrationnode via a needle probe connection to an unbonded pixel, in the manner discussedwithin the text.

To evaluate the linearity of the analog portion of the data stream and to verify

that it is possible to combine this data with the digital response in a smooth

161

fashion, one would like a stable current source capable of generating the equivalent

signal of a few thousand 10 keV x-rays in a reasonable amount of time. Fortunately,

as we will see, such a source is readily available in the form of the leakage from the

Mixed–Mode PAD detector diode. To understand how the detector’s dark current

can become a good weak signal calibration source, we need to look at how this

current is generated.

Hybrid Temperature [deg. C]

Dio

de

Lea

kage

[mV

/pix

el/s

]

-30 -20 -10 0 10 20 30 40102

104

106

Figure 6.2: Average per-pixel leakage current from observed by interior pixels ofa Mixed–Mode PAD hybrid as a function of temperature. The dependent axis isplotted in terms of mV/pixel/second, because this is what is directly measuredfrom the integrator. The direct conversion to charge depends on the absoluteconversion factor of the integrator in each pixel, which, in turn, depends on thesize of the integration capacitor. The integration capacitor was laid out have acapacitance of 50 fF, however, measurements indicate that its actual capacitanceis 20% to 30% larger than expected.

The Mixed–Mode PAD detector diode leakage current consists of a combina-

tion of generation current from within the detector depletion region and diffusion

current from the quasi-neutral areas at the depletion region boundary. As such,

the total leakage current (Jlkg) is given by

Jlkg =

∫∂depn

dx2 q

√Dh

τh

n2i

ND

+

∫dep

dx3 qniGh, (6.1)

where the first integral is over the area of the quasi-neutral region within the n-

type silicon and the second integral is over the complete volume of the depletion

162

region. The first term in this expression is associated with the diffusion current

and the second is the thermal generation current, as described by Shockley-Read-

Hall recombination [64]. Of the parameters within this expression, the dominant

external influnce comes in through the intrinsic carrier concentration (ni) along

with the depletion region volume and bounding. The intrinsic carrier concentration

is dependent on the detector temperature via

ni ∝(T

300

)3

exp

{− EG

2kT

}, (6.2)

while the dimensions of the depletion region are determined by the diode reverse

bias voltage [93]. If these are kept stable, then fluctuations in the detector leakage

current will be governed by the detector shot noise, which, as a Poisson process,

will exhibit integral fluctuation of

δJlkg =√qJlkgtexp, (6.3)

where Jlkg and texp denote the detector diode leakage current and exposure duration

respectively. The average per-pixel leakage at 20 deg. C was measured to be ∼ 300

fA; for pixels within the array interior, this source should exhibit fluctuations of less

than 0.5 fA·√s. Thus, so long as the high voltage and temperature are sufficiently

stable, it is possible to use the diode leakage to test the analog linearity of the

imager.

Achieving thermal and bias voltage stability with this detector is relatively

straightforward, as studying a hybrid within its camera enclosure provides for

these. Care, though, needs to be taken to ensure that no light may enter the

camera while the measurement is made, so the window needs to be covered with

an opaque material. The first test measures the linearity of the analog response

by investigating a single pixel under the influence of the detector leakage. The

temperature of the detector was set to 20.0 ± 0.2 deg. C and held there by a

163

Voutp

[V]

[s]0 0.1 0.2 0.3

0

0.5

1

1.5

2

(a) Voutp Extended Range

Voutp

[V]

[s]0 0.05 0.1 0.15 0.2

0

0.5

1

1.5

2

(b) Voutp Linear Range

Figure 6.3: Traces from a pixel integrator output under the stimulus of the diodeleakage current. Panel (a) was taken with Vref , Vlow, and Vth set to extend the rangeof Voutp into the nonlinear region of the integrator. In panel (b), Vref , Vlow, andVth were set to show the linear range of the integrator. Under normal operatingconditions Vref , Vlow, and Vth are set so that the integrator output will remain withina ∼ 1 V subset of this range. In both panels a linear fit is shown to illustrate theintegrator linearity or deviance therefrom.

thermoelectric within the cryostat. As discussed in section 4.2.1.3, there is a

portion of the range of the integrator output where its response is not linear, as

illustrated in panel (a) of figure 6.3. However, as panel (b) of figure 6.3 shows,

there is a sufficiently large linear range of the integrator response to meet the 1 V

of linear slew specification. For the measurements reported here care was taken to

ensure that the integrator output was set within the linear operating range.

The final step of the linearity test involves showing that it is possible to merge

the analog and digital data sets in smooth fashion. From the discussion in section

4.1, the equivalent voltage (Veqv), that is the voltage that the analog output would

ideally slew if no charge removals occurred, is given by

Veqv =dVeqv

dNΔQ

NΔQ + Voutp. (6.4)

When the stimulus is constant, with the exception of the brief discontinuity when

164

0 0.5 10

0.5

1

1.5

Integration Time [sec]

Vou

t [V

]

(a) Raw Analog Data

0 0.5 10

5

10

15

Integration Time [sec]

NΔ

Q [

N]

(b) Raw Digital Data

0 0.2 0.4 0.6 0.8 1

0

2

4

6

8

10

12

14

16

Integration Time [sec]

Inte

rsca

led

Ana

log

and

Dig

ital D

ata

[V]

(c) Combined Analog and Digital Data

Figure 6.4: Typical analog (Voutp), digital (NΔQ), and merged (Veqv) data for onepixel from leakage current integration series. Detector was held at 20 deg. C,isolated from ambient light during these exposures.

165

charge is removed, the rate of change in the analog residual voltage and the rate

of change in the equivalent voltage are related by

dVoutp

dt=dVeqv

dt. (6.5)

In addition, when the stimulus is constant

dVeqv

dt=

Veqv(t1)− Veqv(t0)

NΔQ(t1)−NΔQ(t0)· NΔQ(t1)−NΔQ(t0)

t1 − t0=

dVeqv

dNΔQ

· dNΔQ

dt, (6.6)

where t1 �= t0 and these times are chosen to be the midpoint of a NΔQ step, i.e. the

average integration time yielding a givenNΔQ value. Then, combining these results

we find that

dVoutp

dt=

dVeqv

dNΔQ

· dNΔQ

dt

⇒ dVeqv

dNΔQ

=dVoutp

dt

(dNΔQ

dt

)−1

. (6.7)

While a single measurement will not yield dVoutp

dtor

dNΔQ

dt, they may be easily ex-

tracted from an ensemble of measurements taken under identical constant stimulus

conditions with varying integration times. This method is illustrated in figure 6.4.

Here, panels (a) and (b) contain, respectively, the analog and digital data from one

pixel for a variety of integration times with the stimulus held constant. The digital

count scaling constant is derived from the ratio of the slopes of the two linear fits,

and the merged data set is shown in panel (c). These data sets were taken using

the leakage from the detector diode at 20 deg. C as a stimulus where, as before, the

camera cryostat was used to maintain the thermal stability of the hybrid and care

was taken to isolate the detector from ambient lighting. The series spans exposure

durations from 500 μs to 1 s with individual integration times randomly ordered to

remove any temporal systematics. Each data point shown represents the averaged

response of 25 consecutive frames taken with identical settings. The full data set

contains 2,000 different integration times taken over the period of a day.

166

Inte

rsca

led

Anal

ogan

dD

igit

alD

ata

[V]

Integration Time [sec]0 0.2 0.4

0

5

10

15

Figure 6.5: Typical merged analog and digital data (Veqv) from one pixel in a Cux-ray tube exposure series. For this series, the tube was operated at 25 kV with acurrent of 0.4 mA, hybrid temperature was set at 20 deg. C. Data scaling factorswere calculated from dark current integration series as discussed in the text.

As a check, both of this interscaling method and as a validation of the front-

end linearity at low signal levels, we utilized our calculations of dVeqv

dNΔQto merge

a similarly recorded data set in which the detector, operated at -35 deg. C, was

illuminated with a flat flood field produced by a Cu x-ray tube operated with a

25 kV bias and 0.4 mA tube current. The results are shown for a representative

pixel from the array in figure 6.5. The signal produced by this flux resulted in

roughly 33 charge removals per second as opposed to 18 with the dark current

alone. If the Mixed–Mode PAD was noticeably nonlinear at low signal rates, as

discussed earlier, then one would expect to see a saw tooth pattern superimposed

upon this ramp. However, as figure 6.5 shows, the interscaling is quite smooth,

with no apparent nonlinearities.

167

6.2 Pixel Electronic Noise

Along with linearity, the electronic noise of individual pixels needs to be evaluated

to understand the pixel-level performance. The purpose of this is twofold: first, it

provides a good assessment of the front end circuit design, and, second, it helps

to decouple effects of individual pixels from pixel-to-pixel variations in assessing

aggregate performance metrics like the detector quantum efficiency.

Fortunately, this measurement is straightforward, as the data from the leakage-

current-based tests of the detector linearity may also be used to measure the de-

tector electronic noise. As mentioned, at each integration time, a set of 25 images

were taken. Within each of these sets and for each pixel, one may calculate a RMS

of the merged analog and digital data. Collecting the RMS calculations for pixels

across the array into a histogram yields a distribution that is statistically Gaus-

sian,2 as figure 6.6 illustrates. This is not surprising, as it merely indicates that

the distribution represents quantities derived from the same statistical ensemble,

which one expects so long as the total signal acquired is not sufficient to bring

out systematic differences in the pixel response or in the leakage currents that the

pixels are measuring.

What is perhaps surprising is the effect that a global correction of the mean

response of the array has on the data. In figure 6.6, the distribution labeled A

shows the uncorrected results for this frame set. Distribution B describes the

same data; however, in it, each image was globally corrected by subtracting off the

image mean before calculating pixel-by-pixel RMS. Figure 6.7 collects this data for

a series of integration times, showing that the system noise response is consistently

2There may be outliers to this distribution (e.g. hot pixels due to surface damage to thedetector or edge leakage, or silent pixels due to unconnected bump bonds) that do not representnormal pixel behavior, but can significantly skew statistical calculations, such as the mean andvariance. By restricting our consideration to the Guassian set of pixels, we automatically cut outthese aberrant elements.

168

[N]

Equiv. 10 keV X-Ray Signal [N]

A

B

0 0.5 1 1.5 2 2.50

500

1000

1500

2000

Figure 6.6: Two pixel RMS distributions derived from the same series of 25 framestaken where all frames had the same integration time. The Gaussian peaked at aright, larger average RMS, was derived from uncorrected data while the Gaussianat the left, smaller average RMS, was corrected for global shifts in the array via amean subtraction. This data assumes a 1 mV = 1 keV conversion gain.

improved by this global correction.

This improvement indicates that there is a source of global noise within the

prototype camera that is significant at low signal levels. There are numerous areas

within the external electronics that could be the source of this noise, including: the

bias on the detector diode, the power supply lines, the current reference from which

the on-chip digital-to-analog outputs are derived, etc. Within the prototype, a full

understanding of this noise source is not essential, as it is easily accounted for in

post processing—so long as it is possible to identify a reference region within each

image with which the global shift may be calculated. This, however, is something

that needs to be evaluated and, if possible, corrected, in the process of building

custom support electronics for the multi-hybrid, large active area imager.

This point aside, figure 6.7 reveals some very interesting points regarding the

weak-signal performance of the Mixed–Mode PAD. First, although the data spans

nearly 20 charge removal operations there are no apparent discontinuities in the

169

noise curve. This indicates that the noise contributed by each charge removal

operation is negligible relative to the noise in the source, the detector diode leakage

current at 20 deg. C. Secondly, the level of the electronic noise is far below the

fluctuation one would expect in the Poisson Statistics of a similar quantity of x-

rays signal. Thus, for flux levels of at least a few x-rays/pixel/s, fluctuations in

the x-ray signal should dominate any measurement.

Equiv. 10 keV X-Ray Signal [N]

Equiv

.10

keV

X-R

aySig

nal

[N]

Raw

Global Shift Corrected

0 500 1000 1500 20000

0.5

1

1.5

2

2.5

Figure 6.7: Detector noise as a function of accumulated diode leakage currentwith the hybrid maintained at +20 deg. C in the camera. To generate this figure,measurement statistics were calculated from sets of 25 images acquired at 1000integration times randomly distributed from 1 ms to 1 s. The range of signalobserved was divided into 75 evenly spaced bins into which the mean per-pixel RMSvalues, based on a Gaussian fit as described in the text, were divided based on theircorresponding mean signal. The data point plotted then indicates the mean, meanper-pixel RMS in each bin and the error bars indicate the RMS fluctuations aboutthis mean. The units on the horizontal and vertical axes are given in equivalent 10keV x-rays (assuming a 1 mV = 1 keV conversion gain) to make the comparisonto an experimental signal more straightforward, although the ordinate axis couldequivalently have been labeled in time spanning up to 1 s.

For signals weaker than this, we may look to figure 6.8 to understand the con-

tribution of electronic noise to the total measurement uncertainty. This figure

describes the fluctuations in measurements of the diode leakage current with inte-

gration time, where the detector was operated at -25 deg. C in a dark environment.

170

Exposure Duration [s]

Equiv

.10

keV

X-R

aySig

nal

[N]

CDS

No CDS

10−2 100 102

10−1

100

Figure 6.8: Detector noise observed over a series of diode leakage current inte-gration extending from 1 ms to 100 s, taken with and without CDS. For thesemeaserements the hybrid was maintained in the camera housing at -25 deg. Cand exhibited an average leakage level 29.5 x-rays/s (assuming a 1 mV = 1 keVconversion gain).

The points on this curve each represents data from a series of 25 images. As dis-

cussed earlier, a global correction was applied to each image based on the mean

signal observed. From this corrected image set, RMS fluctuations for each pixel

were calcuated and histogrammed. This histogram was then fit to a Guassian,

with the resulting centroid and width of this fit used for the data points and error

bars in figure 6.8. Data sets were taken both with and without analog CDS. In

agreement with our discussion from section 4.3.2, the benefits of analog CDS are

small but present up to time scales of a few seconds.

If one could assume that the full signal from each x-ray was observed by a single

pixel, then, based on our discussion in section 2.3, the uncertianty contributed by

fluctuation in the signal from each x-ray will be negligable, for the weak x-ray

fluxes we are considering, in comparison to this noise source. Consequently, for a

dark hybrid at -25 deg. C, the uncertainty in a measurement of N x-rays over t s

will be the electronic noise fluctuations from figure 6.8. In this idealized case, one

171

should be able to confidently measure quantized sets of x-rays up to integration

times of nearly a minute or farther, in the event the analog oversampling discussed

in the conclusion to chapter 4 were implemented.

Unfortunately, this picture is complicated by the fact that the x-ray signal may

be distributed between more than one pixel as a result of the spreading of the

photocurrent as it drifts through the detector diode. The characterization and

analysis of this spreading are the subject of the next two sections (sections 6.3 and

6.4) followed by the impact of this effect on the measurement accuracy in section

6.5.

6.3 Charge Collection

Having verified the linearity of individual pixels and developed a picture of the

noise performance that can be expected from the pixel electronics, we may begin

to look at the quality of images produced by the imager. This begins with an

assessment of the detectors signal collection characteristics.

As discussed in section 2.2.2, when x-rays convert to charge carriers within

the detector diode, diffusion of the generated carriers causes a notable lateral

spreading of the photocurrent signal, the extent of which depends predominantly

on the detector’s detector diode bias and, to a lesser extent, on the temperature

of the diode layer (through its effect on the diffusion coefficient). This phenomena

is illustrated in figure 6.9, which shows the raw x-ray beam from a Cu rotating

anode source, masked to produce a roughly circular illumination field, slightly

larger than a typical diffraction spot, at differing high-voltage settings. Figure 6.10

offers a more direct illustration of the effect’s magnitude, showing the changes in

the amplitude profile along a line taken through the spot center at differing bias

voltages. It should be noted that above ∼100 V the profile of the spot changes very

172

-2 0 2

-2

-1

0

1

2

(a) 3 V

-2 0 2

-2

-1

0

1

2

(b) 5 V

-2 0 2

-2

-1

0

1

2

(c) 10 V

-2 0 2

-2

-1

0

1

2

(d) 20 V

-2 0 2

-2

-1

0

1

2

(e) 30 V

-2 0 2

-2

-1

0

1

2

(f) 60 V

-2 0 2

-2

-1

0

1

2

(g) 90 V

-2 0 2

-2

-1

0

1

2

(h) 120 V

-2 0 2

-2

-1

0

1

2

(i) 180 V

Figure 6.9: Multipixel x-ray spot generated by a Cu target rotating anode source,imaged at differing detector diode reverse bias voltages. Images were acquired withidentical integration times and are shaded using the same logarithmic grey scale,to bring out both faint and intense features. Vertical and horizonal axis units aremm.

173

[mm]

Equiv

.10

keV

X-R

ays 3 V

10 V

30 V

60 V

90 V

180 V

-1 -0.5 0 0.5 10

2

4

6

8

Figure 6.10: From selected images in figure 6.9, x-ray spot intensity profile takenalong a vertical line through the center of the pixel, for differing detector diodereverse bias voltages.

little with increasing bias. Calculations suggest that, at this reverse bias voltage,

the detector diode layer is nearly fully depleted.

While reducing the high voltage blurs the incident signal by redistributing it

over a larger number of pixels, the total amount of charge collected is not signifi-

cantly diminished. This is shown in figure 6.11, which depicts the total integrated

dose from a flood field source as a function of the detector diode bias. The de-

crease in efficiency as the detector diode bias falls below the full depletion level of

∼100 V is explained by the growing size of the detector diode’s undepleted region.

Recalling the discussion of the diode structure from section 2.3.1, the diode’s P/N

junction occurs on the side of the wafer opposite the face where x-rays enter. As

a result, when the diode is not fully depleted, the undepleted region is located

between the x-ray source and the depletion region. This undepleted region lacks

the strong electric field, present in the depleted region, that rapidly sweeps charge

carriers to the integration node of the pixel. Instead, the carriers diffuse until they

either fall into the depletion region or recombine. As the size of the undepleted

174

Detector Diode Bias [V]

Inte

grat

edSig

nal

Nom

aliz

edatV

HV

=15

0V

0 50 100 150 2000.99

0.992

0.994

0.996

0.998

1

1.002

Figure 6.11: Total acquired dose, integrated across the full detector, of a floodfield as a function of detector diode bias. The flood field was generated by aCu x-ray tube biased at 25 kV and the integration time was held constant over allmeasurements. Results are normalized to the dose measured at a bias of VHV = 150V.

175

region grows with reduced bias voltage the likelihood that a carrier will recombine

before reaching the depletion region increases, resulting in the small reduction in

charge collection efficiency shown in figure 6.11.

[mm]

Nor

mal

ized

Col

lect

edD

ose

-0.1 0 0.10

0.5

1

(a) Left Pixel

[mm]

Nor

mal

ized

Col

lect

edD

ose

-0.1 0 0.10

0.5

1

(b) Center Pixel

[mm]

Nor

mal

ized

Col

lect

edD

ose

-0.1 0 0.10

0.5

1

(c) Right Pixel

[mm]

Nor

mal

ized

Col

lect

edD

ose

-0.1 -0.05 0 0.05 0.1

0

0.2

0.4

0.6

0.8

1

(d) Combined

Figure 6.12: Mixed–Mode PAD charge collection. These figures show the chargecollection from a 75 μm spot source of x-rays as it is translated along a line nearthe bisector of three pixels sharing the same row. Panels (a), (b), and (c) show thedose collected in each pixel normalized against the average of the sum of the dosemeasured in the three pixels at each spot location. These individual measurementsare combined in panel (d) along with the sum of the dose measured in the threepixels at each spot location (denoted by the open circles with error bars). Thismeasurement indicates that no charge is lost in the regions between pixels.

Although charge may not be lost by the diode layer the total carrier yield from a

single x-ray conversion may not be completely collected by a single pixel. Between

any two, three, or four adjacent pixels there is a region wherein photocurrent may

split between these pixels. This effect is illustrated in figure 6.12, which shows

176

the collected signal within a pixel and two of its neighbors as a 75 μm spot is

translated in 5 μm steps across the detector. If conversion gain and distortion

effects are correctly accounted for, then the total signal collected will be constant.

6.4 Spatial Response and Resolution

The preceeding discussion of signal collection is sufficient to describe the imager

spatial response for much of the work that will be done with the Mixed–Mode

PAD. This is because, for many of its intended applications, most notably protein

crystallography, the role of the Mixed–Mode PAD will be to measure the position

and intensity of discrete spots or rings of x-ray signal. For these applications,

one generally does not need an understanding of the imager spatial response that

extends beyond the extent to which flux incident at a point on the diode above one

pixel is detected by its neighbors. However, applications producing extended and

complex patterns, as one can find in x-ray tomography, require a more detailed

understanding of the imager’s spatial response.

This section presents an evaluation of the spatial response of the Mixed–Mode

PAD directed at both these concerns. It begins with a discussion of the effect

that discrete sampling and limited imager active area have on the observed sig-

nal, particularly its spectral representation. We then discuss data collection and

refinement methods used to study the pixel spatial response with sub-pixel resolu-

tion. This leads to an evaluation of the spatial and spatial frequency response of

individual pixels, concluding with a discussion of inhomogeneity in the response of

different pixels.

177

6.4.1 Discrete Sampling of Limited Active Area

Pixel Array Detectors, as fixed-grid discrete sampling devices, present a problem

for imaging applications because of the discrepancy between the extent of the diode

impulse response and the pixelation effects of averaging and discrete sampling.

Traditional metrics for evaluating the imager’s spatial response, such as the point

spread function and modulation transfer function, are poorly defined for sampled

image systems [74]. These metrics were created to characterize continuous imaging

systems, e.g. film [54], where the imager response is assumed to be translation

invariant (isoplanatic), so that the image of a point source is independent of its

location. In the Mixed–Mode PAD and other discrete sampling imagers, this

symmetry is broken by the pixel grid. While this effect is not new, with extensive

discussion in the literature extending back into the early 1980s ([74], [31], [81], and

references therein), the problem is particularly acute for the Mixed–Mode PAD,

because the lateral extent of the detector diode’s impulse response (20–30 μm

under typical bias conditions) is much smaller than the pixel geometry (150 μm ×150 μm). As a result, the pixel geometry and the effects of discrete sampling are

the dominant factors determining the imager spatial response.

To evaluate the effects of pixelation on the imager spatial response we begin

with an analysis of the impact the discrete sampling grid has on the spectral

transfer function (hdet) of the imager. From introductory digital signal processing

theory, it is well known that the spatial limit of a discrete set of uniformly spaced

samples of a waveform is given by the Nyquist Frequency (fnyq) of the set:

fnyq =1

Tsamp

, (6.8)

where the sampling period (Tsamp) is twice the distance between samples (�pix).

At frequencies above this limit, the imager may have sensitivity, but the sampling

grid is not capable of accurately representing this response. This occurs because

178

uniform sampling makes the Fourier Transform of the sampled data set periodic

with period fnyq, causing signal aliasing with spatial frequency beyond the Nyquist

Limit into the sampled spectral range.

Whether or not aliasing is an issue depends on how responsive the imager is to

spatial frequencies beyond the Nyquist Limit of the sampling grid. This, in turn,

depends on the continuous response of the system (hdet) which may be written, in

one dimension under the assumption that the system is separable, as

hdet(x) = hpix � hdio(x), (6.9)

where hdio represents the impulse response of the diode detector layer and hpix

represents the binning effect of pixelation. To remove discrete sampling effects,

hdet is defined continuously in x; effectively equivalent to the spatial response of

a composite image built up by merging frames with detector translations so that

there is always a pixel whose center is at x. In this case, hpix will be

hpix(x) = Θ �pix2

(x), (6.10)

where Θ is the boxcar function defined in section 4.2.2.2. From the convolution

theorem of Fourier Analysis we know that the spectrum of hdet (hdet) is the product

of the spectra of hpix (hpix) and hdio (hdio), i.e.,

hdet(f) = hpix(f) · hdio(f). (6.11)

The Fourier Transform of hpix is

hpix(f) =sin(π�pixf)

π�pixf, (6.12)

which has significant amplitude beyond the Nyquist Limit. The exact form of hdio

is generally quite complicated and thankfully unnecessary for the present work.

Knowing that the spatial extent of this response (�q), effectively the spread of the

179

x-ray photocurrent within the diode, is much less than the dimensions of the pixel

(�pix) tells us that

fnyq =1

2�pix

<1

�pix

<1

�q, (6.13)

which implies that hdio must have significant frequency response at least out to

1�q

. This lets us conclude that hdet will have significant frequency response beyond

the Nyquist Limit of the sampling grid, and, thus, aliasing effects should not be

neglected.

A second problem arises, at the other end of the spatial spectrum, when one is

interested in obtaining a spatial frequency spectrum from the imager. If the spatial

signal extends beyond the boundaries of the imager active area, acquiring an image

effectively imposes a sampling window onto the data [78], [44]. Mathematically

this sampling window is represented by the boxcar function (Θτ ) mentioned earlier

in this section. Generally the signal that is discretely sampled may be written as

the product of a sampling window (w) and the distribution of x-ray flux (Φ). Again

appealing to the convolution theorem we have that

w · Φ = w � Φ, (6.14)

which shows us that windowing results in a convolution of the spectra we are

interested in with the spectra of the sampling window. This convolution can cause

the leakage of power within one spectral frequency into neighboring frequencies

leading to distortion of the spectra of interest.

6.4.2 Data Collection and Refinement

We employ a method adapted from [81] to study the response of the Mixed–

Mode PAD beyond the Nyquist Limit of its sampling grid. A series of images are

taken in which the detector is translated in sub-pixel steps across features in the

180

illumination field over a distance greater than the width of a pixel. Data from

these images are then combined, in two steps, to produce a map of pixel position

vs detected intensity. The first step of this combination procedure is to divide each

image into sets of pixels representing the same local illumination field, e.g. rows

of pixels perpendicular to a knife edge or individual spot profiles from a pinhole

mask, taking into account the translation offsets. In the second step, a reference is

determined for each local image subset allowing these local images to be overlaid,

producing a combined image of the local illumination field with finer sampling and

good statistics.

The resulting single image has high spatial resolution but nonuniform sample

spacing and noise with too high a spatial frequency to transform without aliasing.

To remedy these problems, some of the spatial resolution was sacrificed to reduce

noise through convolution with a filter, in the process resampling the data onto

a uniform grid. Our choice of filter is governed by a desire for a broad spectral

response, to minimize the distortion of the signal, with a sufficiently rapid fall off

at and above the Nyquist Frequency to prevent aliasing. The filter used for this

purpose is

hflt(x) =1

2λexp

{−|x|λ

}, (6.15)

where λ is the filter parameter, generalizing to 2D by replacing x with the distance

between the resampling point and the data point. The 1D spectral filtering this

yields is

hflt(f) =1

1 + (2πλf)2. (6.16)

Practically, the filter convolution was carried out in Matlab by defining a new

sampling grid and estimating the value of the integrated product of the filter,

centered on that point of the grid, with the imager response through a discrete

integral of the large number of samples in the combined image.

181

The final step of image refinement involves removing the spectral leakage effects

associated with the limited imager active area. The typical technique for removing

spectral leakage is to use a windowing function with more desirable characteristics

[44]. A variety of alternative windows [44] are available each with merits in terms

of minimizing leakage, amplitude fidelity, and frequency resolution. As we are not

trying to isolate peaks, the frequency resolution of the window is not as important

as the amplitude accuracy and minimizing spectral leakage, so the frequency anal-

ysis presented here employs the Blackman Window [44], which offers good response

in these areas.

Throughout this work, Matlab was used as an analysis platform.

6.4.3 Spatial Characterization Measurements

To experimentally determine the imager’s spatial response, a uniform x-ray source

is occulted by various masks to produce an illumination field on the imager with

known spatial and spectral characteristics. For these experiments, a flood field

was generated by a Cu x-ray tube3 operated at a 25 kV bias with a 0.4 mA

tube current.4 The occultation masks used were a commercial resolution target,5

offering a knife edge mask and bar-target series, and a custom 50 μm tungsten

sheet with a widely spaced grid of 75 μm holes. Images of the illumination fields

were taken with the detector translated relative to the field by a high-precision

translation stage.6 Data sets were acquired, merged, and refined according to the

method outlined in section 6.4.2.

3Model TFS-6050Cu tube with TCM-5000M power supply (Truefocus–Watsonville, CA).4At these settings, the bremsstrahlung spectra will extend up to 25 keV, which will result in

some flat-field transition. The effect of this is a very small, uniform increase in the backgroundlevel across the chip. This effect may be easily corrected for during image processing by applyinga global mean correction to the nonilluminated regions.

5Model 07-525 (Nuclear Associates division of Victoreen–Carle Place, NY), lead thickness0.03 mm.

6Model ESP300 controller with ILS150 and ILS100 linear travel stages (Newport–Irvine CA).

182

In mask measurements such as these, it is important to consider the effects

of a non-ideal flood field, resulting from an extended x-ray source and limited

separation of this source from the pattern mask and imager, upon the resulting

illumination field. A non-ideal flood field distorts the image measured by the

detector in two ways: first, as discussed in section 2.3.1, inclined x-rays will produce

a response in the imager with larger spatial extent than normally incident x-rays;

second, the conjunction of the non-ideal field and the mask will result in parallax

effects.

To evaluate the first effect, we begin by noting that all of the measurements

made in this section were taken within 4 cm of the central axis of a 1 m collimator.

As a result, no x-ray should have entered the detector diode at an incidence angle

of greater than 2.3 degrees. Within the Cu tube spectra the signal from the

Kα emission line dominates both the flux spectral distribution and charge yield

profile, as discussed in section 2.3.1, measured by the Mixed–Mode PAD. Using

the modeling method discussed in section 2.3.1, we can estimate the broadening

of the Cu Kα peak (8.05 keV) resulting from this incidence angle to be ∼ 1 μm,

which is below the resolution of our experiment.

The effects of parallax may be estimated by considering the geometry of: the

flood field, in terms of source size and collimator length; the mask, in terms of

hole size and position, and the imager distance. To simplify this problem, one may

reduce it to one dimension by considering the illumination field in any plane inter-

secting both the source and a hole in the pattern mask, as shown in figure 6.13.7

7This model makes some assumptions that will not hold for a real mask; specifically, it assumesideal edges of the hole and a perfectly opaque mask material. If we were to introduce theseadditional elements, they would effect a small blurring of the edges of the dO and dI regionsalong with an overall background shift dependent on the mean transmission of the mask. Giventhe material and dimensions of the masks used for these measurements, the blurring of theedges of the dO and dI regions is expected to be negligible and we have already discussed howbackground shifts induced by uniform transmission through the mask may be corrected for. Thus,this model should suffice for the measurements presented here.

183

Figure 6.13: Parallax model used for the derivation of equations 6.17, 6.18, and6.19.

184

From this, one sees that the masked image will have a central region (C) of full

illumination as well as an inner and outer boundary regions of partial illumination

(I and O resp.). The size of these regions is given by

dO =hD

hC + hM

ds, (6.17)

dC = dW +hD

hC + hM

(dW − dS)

− hM

hC + hM

(dP +

dS

2

)− hM(hM + hD)

hC(hC + hM)

(dP +

dS

2

)∼= dW +

hD

hC + hM

(dW − dS) , (6.18)

dI =hM + hD

hC

dS, (6.19)

where the variables are defined by figure 6.13. It should be noted that these

formulas do not provide the total parallax distortion from consideration of a single

plane. A complete evaluation of the distortion would require an integral over

all planes that intersect both the hole and the mask, which is a difficult task to

parameterize much less undertake and, thus, not what these formulas are useful

for. The utility of these formulas instead comes from their ability to set limits on

the total parallax distortion based on the worst-case geometry of the hole.

For the flood field measurements presented here, the collimator length (hC)

was 1 m and the x-ray source size (dS) was ∼ 180 μm. With each measurement

presented in the following sections, we will use these values along with the rele-

vant mask parameters and the formulas above to compute the maximum parallax

distortion and thereby estimate the effect of parallax on the measurement.

6.4.3.1 Spatial Response Curves

For diffraction and other applications where the minimum feature size of inter-

est is larger than twice the pixel spacing, so that one does not need to consider

Nyquist Limit sampling effects, the real space response curves provide the most

185

useful metric of the imager’s spatial resolution. In these response curves, the main

consideration is the sensitivity of a pixel centered at one location within the ar-

ray to x-rays incident on the imager at various relative positions. In an idealized

PAD, 100% of the photo-current signal yielded by each x-ray would be detected

by the pixel below, assuming the x-rays are incident from above, the point where

the x-ray enters the diode. In a practical PAD, the variation in interaction depth

and incidence angle, discussed in section 2.3.1, and diffusion of the charge as it

travels through the detector diode layer, discussed in section 2.2.2, result in pixel

sensitivity outside of geometric pixel boundaries. Measurement of two basic re-

sponse curves, the pixel spot response and the edge-spread response, may be used

to derive the fundamental spatial response of the Mixed–Mode PAD.

The purpose of the first measurement is to examine the structure of the ensemble-

average pixel response to x-rays incident on the imager at a given relative location.

The measurement is made by occulting a flood field with a mask containing an

array of widely spaced holes, relative to the pixel width, to produce spots whose

width (∼ 75 μm) is less than half that of the pixel. The imager is then rastered

across this illumination field in translations smaller than the spot width (25 μm)

over an area that spans more than a full pixel (400 μm × 400 μm). An example

of the spot pattern produced at a signal location is shown in panels (a) and (b)

of figure 6.14. To evaluate the effects of parallax in this experiment, we note that

the imager was well centered along the source axis, so that the entire image was

within ±1.4 cm of this axis, in both the horizontal and vertical. Using 2.0 cm as

a limit on the maximal displacement of any spot (dP ), a imager to mask sepa-

ration of 2.0 cm (dD), and the other parameters from section 6.4.3, we find that

dC = 71.4−1.5 μm, where the 71.4 μm value represents the spot size reduction due

to the source size and is common to all pixels within the array and 1.5 μm repre-

186

[mm]

[mm

]

-5 0 5

-5

0

5

(a) Single Image (full)

[mm][m

m]

-1 0 1

-1

0

1

(b) Single Image (zoom)

[mm]

[mm

]

-5 0 5

-5

0

5

(c) Merged Image (full)

[mm]

[mm

]

-1 0 1

-1

0

1

(d) Merged Image (zoom)

Figure 6.14: Spot pattern images taken with the Mixed-Mode PAD when illumi-nated with an x-ray flood field occulted by pin-hole mask. In these images, theholes on the 50 μm thick Tungsten mask are 75 μm in diameter arranged in a gridwith 1 mm × 1 mm spacing. Panels (a) and (b) depict a single image while panels(c) and (d) represent a filtered combination of many images in which the detectorwas translated in sub-pixel steps relative to the pattern of spots.

187

sents the additional reduction due to the spots displacement from the normal axis.

The other parallax parameters, dO and dI , are also constant across the array with

value dO∼= 3.6 [μm] ∼= dI . This level of distortion is at the limit of the accuracy of

the measurements presented in this section and, thus, may be neglected.

Using the method outlined in section 6.4.2, we combined these images to pro-

duce a composite image, shown in panels (c) and (d) of figure 6.14, in which

individual spots may be easily located and analyzed to identify reference points.

These reference points are then used to overlay the raw data from spots across the

imager, creating an ensemble of responses. From this, the ensemble-mean response

is extracted using the filtering operation described in section 6.4.2, producing the

result in figure 6.15.

Because of the finite extent of the spots in the illumination field, this image

does not directly represent the point source response of the pixel. Instead, the

pixel point source response is blurred by convolution with the stimulating spot,

producing the Pixel Spot Response (PSR). Methods exist to deconvolve the effects

of this stimulus, either with Fourier Analysis techniques or direct deconvolution

algorithms. However, both these approaches have limitations.

The Fourier Analysis method is particularly sensitive to the model used for

the stimulating spot. To illustrate this point, consider the response of a pixel

when the spot is moved across a line that bisects its vertical axis. This lets us

represent the stimulating spot with only the horizontal location (x) as a variable.

If we assume that the spot is a perfect circle of illumination of radius R = 36

μm, then the profile in x will be Φ(x) = 2 cos(

πxR

), for x ∈ [−R,R], and zero

otherwise. This is equivalent to windowing the 2 cos(

πxR

)response with a boxcar

function, i.e. Φ(x) = ΘR(x) · 2 cos(

πxR

). Following similar arguments to those in

the discussion of windowing presented in section 6.4.1, we see that the effect of

188

[mm]

[mm

]

-0.1 0 0.1-0.1

-0.1

-0.1

0

0

0.1

0.1

(a) Response Curve – 2D

-

[mm][mm]

PSR

-0.10

0.1

-0.10

0.1

0

0.5

1

(b) Response Curve – 3D

PSR

[mm]-0.1 0 0.1 0.2

0

0.5

1

(c) Horizontal

PSR

[mm]-0.1 0 0.1

0

0.5

1

(d) Diagonal

PSR

[mm]-0.1 0 0.1 0.2

0

0.5

1

(e) Vertical

Figure 6.15: Pixel Spot Response (PSR) to illumination with a flood field occultedby a 75 μm circular aperture. The ordinate axis of both panels (a) and (b) are alongthe imager’s row/column axes. Slice profiles taken horizontally (c), diagonally (d),and vertically (e) through the 2D response function illustrate the symmetries ofthe system.

189

this is

Φ(ω) = ΘR � 2δ(ω ± πx

R

)=

sin(ω + πx

R

)(ω + πx

R

) +sin

(ω − πx

R

)(ω − πx

R

) , (6.20)

which is essentially the sinc response of the boxcar function’s fourier transform,

reproduced at two points via the convolution. An alternative windowing function

(w), offering perhaps smoother response at x = ±R, would still transform as

Φ(ω) = w � 2δ(ω ± πx

R

). In this way, the transform of our choice of window

becomes the dominant element of the deconvolution, making it difficult to produce

an objective result.

[mm]-0.1 0 0.1

0

0.2

0.4

0.6

0.8

1

1.2

(a) Single Sided Deconvolution

[mm]-0.1 0 0.1

0

0.2

0.4

0.6

0.8

1

1.2

(b) Double Sided Deconvolution

Figure 6.16: Discrete deconvolution of the pixel spot response. Panel (a) shows adeconvolution initiated at the left and carried out over the whole data set. Theincreasing fluctuations in the resulting deconvolution are due to noise amplificationeffects that result from the recursive form of the algorithm. Panel (b) shows theresult of two half deconvolutions initiated from either side of the data set. Thismethod gives an accurate representation of the extent of the pixel point sourceresponse; however, it still suffers from error amplification in its interior region. Inboth panels, a dashed line is included to indicate the pixel spot response.

Discrete deconvolution algorithms are less sensitive to the choice of illumination

profile yet more sensitive to error within the data. This is a result of the recursive

190

form of standard discrete deconvolution algorithms. Generally if the convolution

is defined by ρ = h � Φ, where ρ is the measured data and Φ is known, then the

discrete deconvolution of h is given by the recursion relation

h(k) =ρ(k)−∑N−1

l=1 Φ(l) · h(k + l −N)

Φ(N), (6.21)

where ρ(1) is the first non-zero sample of the measured response and h(i) = 0

for all i ≤ 0. Because of this recursive definition, error introduced in early terms

is propagated and magnified in later terms, as illustrated in panel (a) of figure

6.15. This problem may be partially overcome by merging deconvolutions begun

at either end of the data set, as shown in panel (b) of figure 6.15. However, this

only improved the data quality near the edge of the deconvolution, leaving the

interior region contaminated with propagated error.

PSR

[mm]-0.2 -0.1 0 0.1 0.2

0

0.2

0.4

0.6

0.8

1

Figure 6.17: Comparison of the measured diagonal pixel spot response profile(dashed line) with the form calculated under the assumption of separability fromthe vertical and horizontal response profiles (dots).

Even without yielding a complete pixel point source response, the pixel spot

response still tells us much about this function. For example, symmetries in

a convolution reflect symmetries within the convolved functions; the left–right,

horizontal–vertical symmetry exhibited in figure 6.15 indicate that the pixel point

191

source response also possess these same symmetries. Similarly, separability of the

convolution will imply separability of the convolved functions. We test whether or

not the pixel spot response is separable by comparing the product of the horizontal

and vertical spot response profiles, shown in figure 6.15, with the diagonal profile.

The result, shown in figure 6.17, very closely matches the direct measurement,

indicating that the assumption of separability that we have been working under is

valid. Noting the symmetries and separability of the pixel spot response allows us

to simplify our problem from deconvolving the complicated 2D pixel point source

response to retrieving this information directly from the much easier to measure

Line Spread Response (LSR).

Pixel Center to Edge [mm]

ESR

-0.1 0 0.1

0

0.2

0.4

0.6

0.8

1

(a) Edge-spread Response

Pixel Center to Line [mm]

LSR

-0.1 0 0.1

0

0.2

0.4

0.6

0.8

1

(b) Line-spread Response

Figure 6.18: Linear averaged pixel response curves. The ordinate axis of bothpanels (a) and (b) are along the row/column axes and assume that the knife edgeof the occultation mask is perpendicular to this axis.

The line spread response involves a second measurement where the imager is

illuminated with a binary step illumination field using the knife-edge mask, dis-

cussed at the beginning of section 6.4.3. For this measurement, the knife edge was

aligned to within 1 deg of the imager’s vertical (column) axis. As translations are

only necessary along the axis perpendicular to the knife edge, fine sampling trans-

192

lations (5 μm) over a large range (250 μm) are reasonable. As this measurement,

in particular, is very sensitive to parallax effects an effort was made to get the im-

ager as close as possible (dD∼= 1 cm) to the mask. As a result, the interior source

distortion (dI) was only 1.8 μm, which is below the accuracy of this measurement.

The other two parallax parameters (dO and dC) are not relevant, as the knife edge

data only has one edge.

The imager response to these translated illumination fields is the imager Edge

Spread Response (ESR), depicted in panel (a) of figure 6.18. Differentiation of the

edge-spread response gives the imager LSR, effectively the imager’s response to

an infinitely thin line of illumination located at the edge of the knife-edge mask.

From the symmetry and separability arguments presented earlier, we can conclude

that the LSR is equivalent to one dimension of the pixel’s point source response, a

conclusion that is supported by comparing the LSR with the direct deconvolution

of the pixel’s point source response from figure 6.16. From the LSR, we find that

the pixel’s response, at a nominal 150 V diode bias, extends at the greater than

10% level nearly 22 μm and at the greater than 1% level nearly 45 μm.

Spatial Frequency[

1mm

]

MT

F

Nyquist Limit

0 10 20 30 40 5010−3

10−2

10−1

100

Figure 6.19: Modulation Transfer Function (MTF) calculated from the imagerLSR.

193

6.4.3.2 Modulation Transfer Function

For systems with spatial features that extend beyond the imager’s Nyquist limit,

as can be found in x-ray tomography, a more complete description of the imager’s

spatial response is needed. This additional information is typically encapsulated

in figure of merit known as the imager’s Modulation Transfer Function (MTF).

The MTF describes how the amplitude of individual spatial frequencies within

an illumination field are altered, typically attenuated, by an imaging device. As

remarked at the beginning of section 6.4.1, the MTF is poorly defined for discretely

sampled systems where the extent of the imager’s impulse response is comparable

to or smaller than the spacing of the sampling grid. Thus, care needs to be taken

in interpreting the results of this section. Within a single image, the Mixed–Mode

PAD is only capable of providing spatial information up to its Nyquist Limit. The

MTF presented here indicates how responsive the imager is to spatial frequencies

beyond this limit. Within a single image, signals present at these higher frequencies

are aliased back into the Nyquist Range, distorting the image. Only when the

detector is translated relative to the illumination field so as to provide a finer

sampling grid, as discussed in section 6.4.1, is this MTF response attainable.

The MTF is a derivative of a more general concept known as the Optical Trans-

fer Function (OTF) that defines the spatial-filtering effect of an optical system on

an illumination field’s spectral distribution [74]. The OTF, though, is more of a

theoretical tool than a measurable quantity as imaging systems are rarely able

to capture the phase component of an illumination field. Yet, analytically it is a

much easier starting point from which to begin an analysis of the Mixed–Mode

PAD MTF. Recalling the discussion from section 6.4.1, the spatial transfer func-

tion of the Mixed–Mode PAD, i.e. the imager’s pixel point source response, may

194

be written as

hdet = hpix � hdio. (6.22)

The OTF of the imager is then given by

hdet = hpix · hdio. (6.23)

The preceding section tells us the 1D form of hdet directly from the LSR measure-

ment. Fourier transforming this returns the 1D OTF whose magnitude, shown in

figure 6.19, is the imager MTF.

This spectral response has some features that are worth noting. To begin, as

predicted by our discussion in section 6.4.1, the Mixed–Mode PAD MTF extends

well beyond the imager’s Nyquist Limit of 0.3−1 1mm

. Within the MTF, periodic

oscillations in intensity are evident. These oscillations are a direct result of the

pixelation of the imager. As was discussed earlier, the OTF of the Mixed–Mode

PAD may be written as hdet = hpix · hdio, where in section 6.4.1 we derived the

form of hpix to be a sinc function with period �pix. This response will have zeros

at the spatial frequencies f = n�pix

for n = 1, 2, . . .

6.4.3.3 Contrast Transfer Function

Due to the potential pitfalls in any discrete Fourier Analysis, it is useful to have an

independent check of our MTF result. This can be provided by a measurement of

the imager Contrast Transfer Function (CTF), which describes an imaging system’s

response to a series of at least three- or four-line targets of equal spacing and width,

with binary transmission characteristics. The CTF measures the peak-to-trough

intensity variation observed by the imager at the fundamental spatial frequency of

the lines (s, in line pairs per mm), or explicitly

CTF(s) =Tmax − Tmin

Tmax + Tmin

, (6.24)

195

where Tmax and Tmin the maxima and minima of the detected amplitude, respec-

tively.

[mm]

Φ[A

U]

0 1 2

0

5

10

(a) 3.10 LPmm

[mm]Φ

[AU

]0 1 2

0

5

10

(b) 5.48 LPmm

[mm]

Φ[A

U]

0 1 2

0

5

10

(c) 12.42 LPmm

Figure 6.20: Real space Contrast Transfer Function (CTF) response at particularspatial frequencies.

For this measurement, the bar series on the commercial x-ray target discussed

in section 6.4.3 was used. As with the knife-edge measurement, the detector was

stepped along the axis perpendicular to the bar series in 5 μm translations over

a full range of 250 μm. Parallax is not as significant an issue for bar series mea-

surements, as it mainly distorts the higher-frequency harmonics instead of the

fundamental harmonic of the series, unless one is interested in trying to recon-

struct the MTF components from the CTF. Still, its effects are worth estimating.

In this measurement, the farthest bar series was within 3.4 cm (dP ) of the normal

axis with a width of 35 μm (dW ) and the mask to imager spacing was ∼ 1 cm (dD).

Based on this, the edge distortion was dO = 1.8 [μm] = dI and the size of the fully

illuminated region was dC = 35 − 1.8 − 2.6 μm, where the 1.8 μm term results

from the source size and is applicable to all the bar series and the 2.6 μm term is

due to the line displacement. These distortions are at the limit of the resolution

of this experiment and, as such, will be neglected.

The CTF method is appealing in its simplicity as targets are easy to obtain and

the data analysis is straightforward. It has the limitation, though, that it is not

a direct measurement of the imager MTF. At a given fundamental frequency, the

196

Tra

nsm

issi

onC

oeffi

cien

t

Spatial Frequency [1/mm]

CTF

MTF

Nyquist Limit

0 5 10 150

0.2

0.4

0.6

0.8

1

Figure 6.21: Comparison of the Mixed–Mode PAD Modulation Transfer Func-tion (MTF), discrete Contrast Transfer Function (CTF) measurements, and theNyquist Limit imposed by the imager sampling grid.

CTF response will be greater than the MTF response due to the additional har-

monic components present in the binary-response spectra. However, as illustrated

in figures 6.20 and 6.21, as the fundamental frequency of the lines is increased,

higher-frequency harmonic components are suppressed, causing the CTF to con-

verge to the MTF.

6.4.4 Spatial Response Inhomogeneity

Up to this point, our discussion has focused on the ensemble-mean pixel response.

In the ideal, the data from a pixelated imager like the Mixed–Mode PAD should

represent the signal acquired from a two dimensional array of equally-spaced and

equally-sized pixels where each pixel responds according to this ensemble-mean.

Practically, this ideal is never achieved in raw data due to distortion effects within

the imaging system. For the Mixed–Mode PAD, image distortions are primarily

the result of inhomogeneities within the detector diode combined with gain and

197

offset variations in the signal processing electronics.

[mm]

[mm

]

-5 0 5

-5

0

5

(a) Cu X-Ray Tube

[mm]

[mm

]

-5 0 5

-5

0

5

(b) Mo X-Ray Tube (Al attn)

Figure 6.22: Background subtracted and mean intensity normalized flat field re-sponse from Cu and Mo x-ray tube sources (25 keV and 30 keV tube bias resp.)as measured with the same Mixed–Mode PAD hybrid biased at 150 V. Both im-ages are shown on a gray scale spanning ±10% of the mean intensity. A ∼1 mcollimator separated the imager from the x-ray source. In addition, a 794 μm Alattenuator was used to suppress the bremsstrahlung component of the Mo spectrawith the main effects evident below 10 keV.

To elucidate the image distortion created by the detector, flood field response

measurements were taken using x-ray tubes with Copper (Cu) and Molybdenum

(Mo) targets separated from the imager by a ∼1 m, air filled, collimator. This

setup produces an x-ray flood field that is uniform to within a ≤ 0.3% linear

gradient across the imager.8 The operating conditions under which this data was

taken utilized a tube current of 0.4 mA with a high voltage bias of 25 kV for the

Cu tube and a tube current of 0.4 mA with a high voltage bias of 30 kV for the

Mo tube. With these parameters, the Cu tube produces a spectra dominated by

the 8.05 keV Cu Kα emission line, with a significant bremsstrahlung component.

The Mo tube produces a spectra dominated by the 17.5 keV Mo Kα emission line,

also with a significant bremsstrahlung component. To suppress the lower energy

8Determined by rotating the source 180 deg. and comparing the image difference.

198

element of the bremsstrahlung spectrum from the Mo illumination field, a 794 μm

Al attenuator occulted the portion of the field on the imager. This effectively

removes the majority of the bremsstrahlung radiation below 10 keV.

The response to a flat field illumination pattern, background subtracted and

normalized to the mean pixel intensity, of both sources as measured by the same

hybrid operated at the nominal detector diode bias of 150 V, is shown in figure

6.22. Clearly evident are arcs of intensity variation that are independent of relative

detector to source position. As we will discuss later in this section, the magnitude

of these intensity variations is strongly dependent on the bias voltage of the de-

tector diode. However, from a figure 6.11, the accumulated signal integrated over

the full array is essentially independent of the detector diode bias, allowing for a

small decrease due to recombination resultant from longer drift times at lower bias

voltages. This indicates that these arcs are due to redistribution of charge within

the detector as opposed to local variations in the detector quantum efficiency or

conversion gain per x-ray.

The explanation commonly given and accepted for these arcs is that they arise

due to electric fields within the plane of the imager, caused by variations in the

bulk doping profile. These variations are, in turn, a result of the process used to

grow high resistivity silicon wafers [100]. Typically, the high-purity, high-resistivity

wafers used for optoelectric detectors are fabricated in a float zone process. In this

process, a rod of polycrystalline material is held above a crystal seed in the growing

chamber. The bottom of the rod is then gradually heated to the point of melting,

causing a ‘float-zone’ of molten silicon to form between the seed crystal and the

polycrystalline rod. This zone gradually advances up the rod allowing a single

crystal to grow behind. Dopants are typically introduced by allowing controlled

amounts of gaseous dopants into the growth chamber, or less frequently through

199

neutron irradiation after growth [103, 80].

tdrift [ns]

dN

Ndt

8.05 keV (Cu Kα)

13 keV

17.5 keV (Mo Kα)

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

Figure 6.23: Calculated profile of the drift time (tdrift) for holes, in a 500 μm diodebiased at 150 V, generated by normally incident x-ray beams of 8.05 keV, 13.0keV, and 17.5 keV, based on equations 2.19 and 2.30. The dotted vertical linesdenote the mean drift time for the curve denoted by their end points (38 ns, 48ns, and 84 ns resp.).

To understand the effect of these lateral fields consider that the mean velocity

(〈v〉) of a charge carrier (e.g. electron) moving in an electric field (E) decomposes

simply as9

〈v〉 = μeE : 〈vx〉 = μeEx, 〈vy〉 = μeEy, 〈vz〉 = μeEz, (6.25)

where μe is the electron mobility (the equations are analogous for holes with the

exception of a change in sign). The motion of carriers in the plane of the detector

is separable from motion through the detector. The magnitude of the arcs then

depends on the magnitude of the fields and the time spent under their influence.

There is little that can be done to reduce the magnitude of these transverse fields

9This assumes that the induced velocity is below the velocity saturation limit. For detectordiode bias voltages within our operating range of 0 to 200 V, this assumption should hold.

200

in commercial wafers—apart from selecting diodes, after hybridization, that ex-

hibit minimal distortion. However, as alluded to earlier in this section, there are

controllable parameters that affect the time spent drifting in these fields. From

equation 2.19, the time spent drifting within a diode depletion region (tdrift) is

dependent on the depth into the diode at which the x-ray is absorbed, the width

of the diode, and the potential across the diode.

As discussed in section 2.3, the profile of absorption depths for a monochromatic

beam of x-rays is strongly affected by the energy of the x-rays. As a consequence,

the profile of drift times depends on the energy; however, this effect is complicated

and nonlinear. In figure 6.22, there is little perceptible difference between the

magnitude of intensity fluctuations in the two flat field images though the spectral

composition and hence absorption profile of the two illumination patterns is quite

different. The explanation for this is a combination of the compression effects of

the diode’s roughly linearly increasing, with depth into the diode, field strength

on the drift times and the limited total thickness of the diode. As illustrated in

figure 6.23, although the attenuation length of 8.05 keV x-rays (λ= 70.89 μm) and

17.5 keV x-rays (λ= 699.02 μm) differs by nearly an order of magnitude, the mean

drift time differs by only 46 ns, roughly a factor of 2.2. Due to the nonlinearity

of the dependence of drift time on x-ray energy, it is possible to create scenarios

where the spectra of the illuminating field would strongly affect the magnitude

of these intensity variations, e.g. very thick diodes, weak reverse bias, or extreme

energy differences. However, within the operating range of the Mixed–Mode PAD

under typical operating conditions, an energy dependence in these distortions will

be difficult to detect.

A more dominant, though less tunable, factor in the magnitude of this dis-

tortion is the thickness of the diode layer. When manufacturing the diodes, it

201

is typically possible to select from a number of different wafer thicknesses.10 At

the same energy and depletion potential, substantially less distortion will occur in

thinner diodes. Thus, in applications where the additional radiation tolerance of

thicker diodes, to be discussed in section 6.7, is not needed, thinner diode layers

are preferable.

Φ(V

dio

)〈Φ

(Vdio

=150[V

])〉

[mm]0 5 10 15 20

0.9

1

1.1

1.2

(a) Vdio = 50 V

Φ(V

dio

)〈Φ

(Vdio

=150[V

])〉

[mm]0 5 10 15 20

0.9

1

1.1

1.2

(b) Vdio = 100 V

Φ(V

dio

)〈Φ

(Vdio

=150[V

])〉

[mm]0 5 10 15 20

0.9

1

1.1

1.2

(c) Vdio = 150 V

Φ(V

dio

)〈Φ

(Vdio

=150[V

])〉

[mm]0 5 10 15 20

0.9

1

1.1

1.2

(d) Vdio = 200 V

Figure 6.24: Intensity profile drawn across the same line on the same hybrid show-ing the variation in distortion with detector diode bias, normalized to the meanintensity at a bias of 150 V. The line shown here was chosen to be roughly normalto the arcs of intensity distortion.

The final external parameter affecting these drift times, and thereby the magni-

tude of distortions, is the potential across the diode. The impact of this parameter

is illustrated in figure 6.24, which shows four plots of the same normalized line

profile at differing detector diode bias voltages (Vdio). While the impact of the

diode bias setting can be strongly seen from these plots, the extent to which this

10Our diode manufacturer (SINTEF–Trondheim, Norway) offered a choice of 300 μm or 500μm diodes.

202

can efficiently minimize image distortion is limited. As we recall from equation

2.19, the relationship between the bias voltage and drift time is inversely linear,

i.e. doubling the diode bias reduces the drift times by a factor of two. Practically

though, there are reasonable limits to how high one may safely increase the detec-

tor diode bias voltage11 and thus the extent to which this may be used to suppress

distortion.

As a consequence, some degree of distortion is nearly inevitable within the raw

data. Section 6.6 discusses the implication of this distortion on the data as well

analysis methods to reduce its impact.

6.5 Detector Quantum Efficiency

Having assessed the performance of the Mixed–Mode PAD at the pixel level and

having considered its spatial response and spatial distortions, we are now in a

position to evaluate the importance of calibration to the detector image quality.

To do this, we employ the Detector Quantum Efficiency (DQE), a figure of merit

commonly used to characterize x-ray imagers [41]. Defined as the squared ratio of

the observed signal to noise over the ideal signal to noise of the source

DQE

(∫Φ

)=

( 〈R Φ〉qVar(

RΦ)

)2

obs( 〈R Φ〉qVar(

RΦ)

)2

src

, (6.26)

it can offer insight into the detector’s ability to reproducibly record an x-ray signal

in terms of the intrinsic fluctuations within the signal. An ideal detector, one

that observes every x-ray produced by the source without contributing any noise

to the measurement, would have a DQE of 1. The DQE is then reduced by the

11Although the breakdown voltage is silicon is high, ∼ 3 × 105 V/cm, one must also considerthe attainable stability of the bias at high voltages, see discussion at the end of section 2.2.3.1,and the potential for arcing in a vacuum environment.

203

extent to which the detector is capable of absorbing the incident radiation, i.e. the

Quantum Efficiency (QE) of the detector, and the extent to which it contributes

to the variation within this measurement. By its very definition, the DQE is a

complicated beast that effectively merges many elements of a detectors response

into a single performance metric.

One most straightforward and telling methods for measuring the DQE of a

detector involves taking a representative point of x-ray flux and repetitively sam-

pling the signal observed from this spot at different locations on the detector (by

translating the detector relative to the illumination field). The choice of spot size,

however, has a nontrivial impact on the results of the DQE measurement due to

the effects of discrete spatial sampling. When compared at equivalent dose per

unit area, large spots, extending over multiple pixels, will exhibit higher DQE at

a given dose level than small spots due to averaging effects that suppress pixel-

to-pixel gain variations and the smaller percent variations in the number of pixels

sampling a spot.12 A sub-pixel spot will exhibit the worst possible DQE, at con-

stant dose per unit area, as this case maximizes the effects of pixel to pixel gain

variations while potentially dividing the x-ray signal between as few as one and as

many as four pixels.

For the Mixed–Mode PAD DQE measurement a Mo x-ray tube source was

used, operated with a high voltage bias of 30 kV and tube current of 0.4 mA. A

791 μm Al attenuator was also used to suppress the low-energy bremsstrahlung

radiation of the source, leaving a spectrum dominated by the Mo Kα line at 17.5

keV (example spectra from this source are shown in section 7.1). After an air filled

flight path of 1 m this flood field was occulted by a 50 μm thick tungsten sheet

with a 1 mm × 1 mm grid of 75 μm diameter holes, resulting in an illumination

12Though, if the same comparison is made strictly in terms of total dose, small spots willperform better at low total dose levels, due to their smaller read noise contribution, though largespots will still outperform small ones once the read noise effects become negligible.

204

pattern on the detector comprised of sub-pixel spots over a very weak (< 0.1%) flat

background, due to transmission through the tungsten sheet. Exposure times were

varied logarithmically from 1 ms to 100 s, with sets of 4 images taken at a total of

25 different locations of the detector relative to the spot field. These displacements

were chosen at random, to remove systematic bias, from a flat distribution in a

2 mm × 2 mm region of the plane perpendicular to the x-ray path.

X-Rays [18 keV]

DQ

E/Q

E2

10% 3% 1%

100 102 10410−2

10−1

100

Figure 6.25: Detector Quantum Efficiency normalized to Quantum Efficiency ofthe detector. The error bars included with the data indicate the distribution ofRMS computed from the individual illumination spots. Due to systematic variationbetween the different spots this RMS is much larger than the fluctuation betweenDQE/QE2 measurements, as evident by the four repeated measurements. Thedashed lines included on the plot represent curves of constant precision, indicatingwhere fixed pattern noise is at a level that the precision of the measurement ceasesto improve with dose. Curves of 10%, 3%, and 1% precision are shown.

To analyze the data, the set of four images at each camera position were used to

identify unintended radiation events.13 Following identification of a clean image,

any residual global fluctuation in the level of the un-illuminated portion of the

detector, i.e. the valleys between the peaks, was subtracted off, in accordance with

the discussion of section 6.2. Within each combined image, illumination peaks were

13A.K.A. Zingers. These may be produced by terrestrial radiation, cosmic rays, etc.

205

identified and correlated with the position of the same illumination field with the

camera at another location. The intensity of each peak was then calculated in each

image. As the source itself exhibited non-negligible, non-Poisson fluctuations at the

level of ∼5%, over the time periods considered, it was necessary to normalize the

intensity of each peak by the total intensity of all peaks in each image. The RMS

of the integrated intensity of each peak, computed over all locations of the peak

from the same illumination spot, was then scaled by the average total intensity

of all peaks over all images. This series of transformations minimizes the error

introduced by the systematic source fluctuation. The average RMS variation of

the peak-by-peak intensity was then taken as the observed intensity variation and

the source variation was then approximated as monochromatic at 17.5 keV with

Poisson statistics. While not completely accurate, this estimate is, at worst, a

lower limit on the noise and thus a lower limit on the resultant DQE. The final

curve, normalized by the quantum efficency of the detector, is shown in figure 6.25.

In interpreting the DQE curve it is useful to consider at a second order poly-

nomial model of the observed noise,

Var

(∫Φ

)= a0 + a1n+ a2n

2, (6.27)

where n is the mean number of x-rays emitted by the source. In this model, the

0th order term (a0) represents the read noise of the detector, the 1st order term

(a1) represents the random noise of the detector and source, and the 2nd order

term represents the systematic noise of the detector. Under this model, a Poisson

source will yield

DQE

QE2 =n

a0 + a1n+ a2n2. (6.28)

This model allows for up to three regions of accumulated dose [95]. In the first

region, the noise of the detector is dominated by the fixed readout noise, with

improving DQE/QE2 with increasing dose. In the second region, the readout noise

206

becomes negligible compared to the combined random noise of the detector and

source. Then, in the third and final region, the systematic noise of the detector

becomes dominant leading to a fall of in the DQE/QE2 response. Referring these

regions to the normalized DQE curve shown in figure 6.25, we observe the initial

readout noise dominated portion rising to the second region. Here, the fact that

the detector’s response peaks at slightly below one tells us that the electronic

contribution to the variance in the observed signal is small in comparison with

the intrinsic fluctuation in the x-ray signal, particularly given that we are likely

underestimating our source fluctuations. Finally, we see the fall off introduced by

systematic error in the measurement.

From the fall off introduced by the detector systematic error, we may estimate

the attainable level of precision for an uncalibrated Mixed–Mode PAD. This is

done by extrapolating the curve in the high-dose region to predict its limiting

curve of constant precision. From the fit shown in figure 6.25, we find that the

uncalibrated imager is limited by fixed-pattern noise to a precision of ∼2.5% for

17.5 keV x-rays. It should be noted, though, that the systematic gain is a function

of the total charge measured, while the number of x-rays observed will ideally

obey Poisson Statistics. Thus, a systematic limit of 2.5% at 17.5 keV corresponds

a systematic limit of ∼1.9% at 10 keV. Improvement beyond this requires post-

acquisition image correction, to suppress or remove these systematics, that will be

addressed in the next section.

6.6 Detector Calibrations and Corrections

From the preceeding sections, an understanding of the characteristics of the Mixed–

Mode PAD has been developed. For the detector to perform beyond this level

requires post acquisition image processing based on careful calibration of the de-

207

tector. This section offers an outline and discussion of potential corrections that

can be applied to Mixed–Mode PAD images and how the detector can be calibrated

to measure these correction factors. However, as the Mixed–Mode PAD is the first

example of a large-area pixel array detector utilizing an integrating front end and,

therefore, this is the first attempt to calibrate such a device,14 this should be seen

as only a starting point for optimizing the detector rather than a complete recipe

book. Future experience with the detector, through regular use, can be expected

to refine and improve upon these techniques.

For most work, correcting the raw data for the Mixed-Mode PAD will entail:

• Merging the analog data (Vres) and digital data (NΔQ) into a single measure-

ment for each pixel, on each exposure, with an appropriate scaling factor

(gdig).

• Removal of pedestal offset variations (Vped).

• Applying an absolute gain calibration (gabs) to relate observed signal to de-

posited x-ray energy.

• Removal of detector-induced image distortion.

The first three elements relate to the total integrated signal observed by the

detector through the relation∫dtΦ = gabs · (gdig ·NΔQ + Vres − Vped) , (6.29)

where gabs, gdig, and Vped are terms that must be individually calculated for each

pixel. The remaining element, the distortion correction, is distinctly different and

will be addressed separately.

14While integrating PADs bear some resemblance to their digital counterparts as well as tophosphor coupled CCD detectors the techniques used to calibrate these devices are difficult toapply to PADs for reasons that will be discussed.

208

In the following sections, each of these correction steps is taken up in detail,

presenting both typical correction data along with a brief discussion of how this

data is obtained.

6.6.1 Analog and Digital Data Combination.

The first calibration step to perform is to combine the analog and digital data from

each pixel into a single measurement. This amounts to choosing a scaling factor,

for each pixel, that converts the number of charge removal operations performed

to an equivalent voltage shift in the analog output. In an ideal environment, this

would simply be the difference of Vref and Vlow; however, due to contributions

from differences between pixels and their respective analog output chains, there is

systematic pixel-to-pixel variation in the analog equivalent voltage of each pixel’s

digital counts. Calibrating the individual contributions to this variation would be

a difficult, time consuming, and tedious task. Instead, it is better to lump these

effects into a direct measurement of the scaling factor (gdig), a similar technique

to that, explained in section 6.1, used to demonstrate the low-end linearity of the

pixel response.

[N]

gdig

〈gdig〉0.95 1 1.050

200

400

600

Figure 6.26: Normalized distribution of scaling factors for combining analog anddigital data from the Mixed Mode PAD.

209

Explicitly, to perform this calibration a series of dark integrations are taken

in which the exposure time is varied randomly to remove systematics due to low-

frequency drift in the leakage current. For the data taken in section 6.1, the

maximum duration of the dark exposure was chosen to be sufficiently long to

allow for at least 10 charge removal operations in every pixel and the number of

trials to be large enough that there was sufficient resolution to map out analog

residual voltages in the range where no removals occur. Consequently, over 1000

separate integration periods were needed (with repetition for statistics) to clearly

map out the slope of the analog and digital data, a quantity that is impractical

for a standard calibration method. For standard calibration, instead of the flat

distribution, we recommend the following a simple algorithm (algorithm 1) for

generating a series of exposure periods, where tana is chosen to cover the span of

the analog residual when no charge removals occur and tdig is chosen to span at

least 10 (though preferably more) digital charge removals:

Algorithm 1 Exposure Times for Mixed–Mode PAD Calibration

1: procedure ExpoTime(tana, tdig) � Generate one exposure period.2: r = random([0, 1)) � Random number: [0, 1), flat dist.3: if r < 0.5 then4: texp = tana · random((0, 1]))5: else6: texp = tdig · random((0, 1])7: end if8: return texp

9: end procedure

With this simple algorithm, less than 100 exposures should provide good sam-

pling of the slopes of the analog and digital data curves. As in section 6.1, the ratio

of the slope of the analog data to the slope of the digital data yields the scaling

factor (gdig) for the pixel. Figure 6.26 shows the distribution of normalized scal-

ing factors from one Mixed–Mode PAD detector hybrid. It should be noted that,

210

along with the pedestal offset, the scaling factor will vary over long, on the scale

of weeks or months, time periods. Thus provisions should be made to recalibrate

this portion of the detector on a regular basis.

6.6.2 Pedestal Offset

The pedestal offset (Vped) is a shift in the measured signal that occurs independent

of the duration of the integration. As with many of the other systematic errors, it

is derived from many sources including clock feedthrough from transistor switches,

such as the reset, CDS, and pixel sample and hold switches, as well as offsets

and gain differences in the various amplification and buffer stages. There are two

methods to easily remove the pedestal offset. If a difference of two images is taken,

e.g. if a background is subtracted from the exposure, then the static variation

within the pedestal will be removed. Where single images must be analyzed the

constant term from the fit of the analog residuals preformed in section 6.6.1 may be

used to remove the static pedestal. Figure 6.27 shows the distribution of pedestal

offsets from one Mixed–Mode PAD detector hybrid.

[N]

Vped [V]0.25 0.3 0.35 0.4 0.45 0.50

200

400

600

Figure 6.27: Distribution of pedestal offsets from one Mixed–Mode PAD detectorhybrid.

211

6.6.3 Absolute Gain

The calibration techniques presented up to now focus on correcting individual

pixels, independently. From the DQE work in section 6.5 this degree of correction

is good to ∼2.5% (for a 17.5 keV source). To increase the detector’s precision

beyond this point, the level of fixed pattern noise must be diminished through

calibration with an external source. In addition, for some experiments, we will

need to be able to relate the data to an absolute quantity—the total x-ray energy

deposited in the detector diode layer.

Unfortunately, measuring the absolute gain of a pixel is non-trivial because

of the coupling between spatial distortions and gain variation in the total non-

uniformity of the imager response. Therefore, in order to correct for these effects,

they must first be decoupled and characterized independently. In devices like

phosphor coupled CCD systems, the spatial distortions vary on long (i.e. mm)

length scales relative to the pixel size. As a result, the canonical calibration method

is to measure an image distortion map by employing a, relatively sparse, grid

illumination pattern and computing the displacement of pattern elements relative

to their expected positions [11]. Once the spatial distortions are corrected, the

phosphor coupled CCD system may be gain calibrated through simple flat field

exposures. In a PAD, however, the spatial distortion occurs through pixel-to-pixel

variation in the total active area of each pixel, as discussed in section 6.4.4, on

length scales near to or less than the pixel size; thus, the traditional method of

utilizing a flat field illumination to determine relative, and sometime absolute,

gains breaks down because there is no way to determine if excess signal seen in a

pixel is due to a variation in the gain of the pixel or variation in total active area

of the pixel.

It was proposed that, despite this, it should be possible to measure the gain

212

using a flat field illumination by taking multiple short frames in which the expected

x-ray occupancy per pixel is less than one. Following the procedure outlined in

section 7.1, the individual reading from each pixel could be histogrammed, with

the idea that two peaks corresponding to zero and one would form. As we will show

in section 7.1, the Mixed–Mode PAD is capable of this level of sensitivity; however,

when the illumination field is broader than a single pixel, charge sharing between

pixels becomes an issue. Studies into this issue indicated that, this is possible

if a high energy, highly monochromatic source is available. However, this work

also indicates that this method is incapable of yielding a calibration that would

improve the detector beyond the 2.5% precision of the uncalibrated fixed pattern

noise. To understand this, consider that the error in this two peak gain calibration

is the sum of the error in the position of the zero and one x-ray peaks divided

by the separation of the two peaks. As our observed, average conversion gain is

only ∼0.7 mV/keV, even the Mo Kα line (17.5 keV) only yields ∼12 mV/x-ray.

Consequently, calibration at the level of 2.5% would require peak measurement at

an accuracy of 0.21 mV in each peak which would be challenging as our analog

digitization is binned in 1 mV steps. Calibration to the precision of 0.25% desired

of the final detector would require an accuracy of 0.021 mV in each peak, not

strictly impossible, but very difficult with this technique.

A better alternative would be the construction of a dedicated calibration field.

This setup would require a flood field of monochromatic x-rays occulted by a mask

of sub-pixel-width, diameter holes spaced to match a multiple of the pixel grid,

e.g. 25 μm holes on a grid of 750 μm × 750 μm centers. If the source is sufficiently

monochromatic, then this setup should allow x-ray spectra to be recorded with

multiple photon peaks. Recording spectra with multiple peaks dramatically re-

duces the accuracy required in determining the location of any given peak, making

213

spectral calibration much simpler. In section 7.1, this technique is demonstrated,

although only a single illumination spot was used as a masks with an appropri-

ate grid spacing was not available. In addition to this mask, for this setup to be

practical, it would be require two linear as well as one angular degree of freedom

between the mask and detector—for mask alignment and translation.

6.6.4 Distortion Correction

The image distortion introduced as the charge drifts through the diode layer is

potentially a substantial source of measurement error. Spatial distortions and gain

variations are closely coupled sources of fixed pattern noise in any imaging detector.

For the Mixed–Mode PAD, detector calibration requires decoupling these two noise

sources via independently measuring correction factors for one, either the spatial

distortion or gain variations may be chosen, after which the other correction may be

determined from flood field analysis. The canonical method of correcting phosphor

coupled CCD imagers is to first measure the distortion correction, by illuminating

the image with a known pattern of spots and mapping the displacement of these

spots relative to their expected location [11]. The length scale on which distortions

occur in these systems is sufficiently large that correction on the mm length scale

is acceptable. This approach is not well suited for PAD detectors, however, as the

image needs to be corrected on length scales that are close to the pixel dimensions.

Because we have a very accurate means of measuring the absolute gain per pixel, as

was discussed in the previous section, we may, instead, measure the gain variation

independently of the spatial distortion and then use an analysis of the flood field

response to correct for spatial distortion.

How to deal with this distortion, however, strongly depends on the type of

measurement being performed. To illustrate this, consider a diffraction exper-

214

iment where one needs to measure the intensity of diffraction spots at various

locations across the detector against a background of diffuse scattering. The inho-

mogeneities in the detector are unlikely to substantially distort the spots directly

but they can have a significant effect on the background that can, in turn, distort

the spot measurement. To see this, suppose that one were trying to measure a

spot whose intensity was half the flat background level. Since spatial distortions

introduce up to ∼3% variations in a flat field, the signal measured from this spot

will systematically vary by 6%, depending on where it lands on the detector. Sim-

ilarly, if the diffraction were twice the intensity of the background, the systematic

variations from spatial distortions would be reduced to 1.5%. For this problem, the

distorted field is effectively a background and so removing it through subtraction

is preferable. Alternatively, if the data of interest extend continuously across the

detector, as for example with x-ray tomography or ring diffraction, then a simple

subtraction will likely not be sufficient, requiring instead a correction transforma-

tion. There are different choices for these, however, that themselves preserve and

distort different aspects of the image as a consequence of their correction.

6.6.4.1 Image Correction Transforms

For an image with extended continuous regions of interest, the problem is more

difficult, as one must contend with a distortion correction that will alter the dis-

tribution of signal between pixels. Because illumination fields and their resulting

images are not isomorphic, it is not possible to construct a correction transform

that preserves all aspects of the original image. Instead, one faces trade-offs be-

tween image aspects, such as the spatial resolution and the signal fidelity of the

detector. In the remainder of this section, we will present two image correction

transforms. The first, which relies on a normalization of the detector’s quantum

215

[mm]

[mm

]

-5 0 5

-6

-4

-2

0

2

4

6

(a) Raw Image

[mm]

[mm

]

-5 0 5

-6

-4

-2

0

2

4

6

(b) QE Normalized

Figure 6.28: Tomography of a section of a $1 bill illustrating the quantum efficiencynormalization distortion correction transform. Panel (a) shows the image originalimage, a merger of 10 100 second exposures using a Cu x-ray tube operated at 25keV and 0.4 mA. Panel (b) shows the effect of applying the quantum efficiencynormalization. There are a four dead pixels in the imager used to generate thisimage. The same data set was used to generate these image as was used to generatethose shown in figure 6.29.

216

efficiency, effectively preserves the spatial resolution of the image at the expense

of accurate measurement of local signals. The second, which uses a signal re-

distribution technique, accurately preserves the total signal observed, though, at

the expense of some spatial resolution. Other correction transforms are certainly

possible, but beyond the limited scope of this work.

The first correction transform that we will consider involves a quantum effi-

ciency normalization. The idea behind this correction is that the differing total

active areas among pixels may be viewed as differing quantum efficiencies, at least

in the case of uniform illumination. So long as there is sufficient dose, this effect

may then be removed by a simple rescaling; in essence, this means that measure-

ments from pixels that collect from a large active area are suppressed while those

that collect from a small active area are amplified, to the end that the detector

yields a uniform response to uniform illumination.

To calculate this correction, one begins by calculating a correction map (C)

from an ensemble mean, background subtracted flat field illumination (Iflat)15 by

way of

C(r, c) =Iflat(r, c)

〈Iflat〉 , (6.30)

where r and c are row- and column-wise indices, respectively, of pixels in the image.

The correction is then applied to a background subtracted, yet distorted, image

(Idist) through

Iqen(r, c) =Idist(r, c)

C(r, c), (6.31)

to produce the final, quantum efficiency normalized, result (Iqen).

As figure 6.28 shows, this correction is an effective means to generate a nice pic-

ture, as it does a good job preserving the spatial resolution of the image. However,

15For all the correction transforms, the reference images need to have sufficient statistics tobe limited by fixed-pattern noise. Otherwise, the error in the reference image will introduceunnecessary uncertainty into the distortion corrected image.

217

there are a few caveats that must be recognized with this transformation. The first

is that the normalization only corrects the mean value of the illumination pattern,

it does not correct the noise. Thus, pixels that collect from a larger total active

area will show greater signal variation than pixels that collect from a smaller total

active area, as a simple consequence of counting statistics, and as a consequence

the level of signal in the pixel is no longer a reliable indicator of the uncertainty of

the measurement. In addition to this, and perhaps more important, the quantum

efficiency normalization does not ensure conservation of signal. As such, it can in-

troduce systematic error into measurements, particularly those requiring accurate

quantification of a signal deposited in an area spanned by only a few pixels.

[mm]

[mm

]

-5 0 5

-6

-4

-2

0

2

4

6

(a) Raw Image

[mm]

[mm

]

-5 0 5

-6

-4

-2

0

2

4

6

(b) AF Signal Shift

Figure 6.29: Tomography of a section of a $1 bill illustrating the charge-shiftingadaptive filter correction transform. Panel (a) shows the image original image, amerger of 10 100 second exposures using a Cu x-ray tube operated at 25 keV and0.4 mA. Panel (b) shows the effect of applying the adaptive filter correction. Thereare a four dead pixels in the imager used to generate this image, these pixels andtheir nearest neighbors are excluded from the adaptive filter. The same data setwas used to generate these image as was used to generate those shown in figure6.28.

An alternative distortion correction transform, that conserves the total signal

218

across the image, may be performed using signal redistribution. Here, the idea

is, effectively, to rebin the image into an array where each element represents an

equivalent total active area by shifting signal between nearest neighbor pixels.

While this may sound simple, determining the appropriate amount of charge to

shift and where to shift it is nontrivial. To accomplish this, we turn to a method

developed in the field of system theory called adaptive filtering [105], where a

recursive algorithm is used to determine a series of parameters (called weights)

that control the correction transform. Based on these weights, a distorted image

(Idist) is transformed into an image where the distortion has, in principle, been

removed (Iaf).

For the algorithm developed for the Mixed–Mode PAD, these weights can be

thought of as corresponding to extent to which one pixel extends beyond, or does

not reach, its ideal boundary with its nearest neighbor. With one weight for each

shared edge, this transform uses 128×127 (for row edges) and 127×128 (for column

edges) arrays of weights to perform the requisite correction. In determining these

weights, the distorted image from a flat field illumination (Iflat), after pixel gain

calibration and background subtraction, is processed with an iterative training

algorithm that uses the absolute value of the row- and column-wise gradient as

an error measure to step the image towards an idealized flat response. In other

words, we posit that the gradient of the corrected image should be zero and then

recursively execute an adaptive loop on the training image (Iflat) that seeks to

minimize this gradient by shifting charge between nearest neighbor pixels.

More rigorously, the training process of the adaptive filter is performed by

letting Iflat = I0 denote the initial flat-field image and Ii(r, c) be the pixel value

of the rth row and cth column element of the ith recursive image. The update

219

algorithm is then16

Ii+1(r, c) = Ii(r, c) + qstp ·[sgn (Ii(r + 1, c)− Ii(r, c))

+ sgn (Ii(r − 1, c)− Ii(r, c))

+ sgn (Ii(r, c+ 1)− Ii(r, c))

+ sgn (Ii(r, c− 1)− Ii(r, c))], (6.32)

where sgn is the sign operator17 and qstp is a step size that determines the rate

of conversion for the training algorithm as well as the resolution of the correc-

tion. Collecting the terms generated by the recursive algorithm we may define the

weights after the nth iteration of the adaptive filter as

an(r,c) = qstp

n∑i=0

sgn (Ii(r + 1, c)− Ii(r, c)) , (6.33)

bn(r,c) = qstp

n∑i=0

sgn (Ii(r, c+ 1)− Ii(r, c)) , (6.34)

where the subscripts a and b denote row- and column-wise weights. Then

In+1(r, c) = I0(r, c) + an(r,c) ·

[(an

(r,c) > 0)? (−1) : (+1)

]+ an

(r+1,c) ·[(an

(r+1,c) > 0)? (+1) : (−1)

]+ bn(r,c) ·

[(bn(r,c) > 0

)? (−1) : (+1)

]+ bn(r,c+1) ·

[(bn(r,c+1) > 0

)? (+1) : (−1)

], (6.35)

where we make use of the ternary conditional operator18 to simplify our notation.

As n grows, the resultant image should converge, at a rate dependent on the size

of qstp, to a flat distribution to within ±4 · qstp at each pixel, thus, in the following,

16In the remainder of this section we will be a little loose with our indices, to keep the descrip-tion as succinct as possible, operating with the understanding that where an indexed elementmay not exist, e.g. at the edges of the the image, the indexing term will be taken as zero.

17Definition of the sign operator: sgn(x) =

{0, if x = 0,x|x| , otherwise.

18Definition of the ternary conditional operator: (A) ? (B) : (C) equals B if A is true and Cotherwise.

220

we will discard the superscript n with the understanding that limn→∞ rn = r and

limn→∞ cn = c.

To normalize these weights so that they may be applied to a general image, we

divide each by the initial signal in the pixel which charge is shifted from,

a(r,c) =a(r,c)(

a(r,c) > 0)? (I0(r + 1, c)) : (I0(r, c))

, (6.36)

b(r,c) =b(r,c)(

b(r,c) > 0)? (I0(r, c+ 1)) : (I0(r, c))

. (6.37)

Then the distortion corrected form (Iaf) of a distorted image (Idist) is given by

Iaf(r, c) = I(r, c)

+ a(r−1,c) ·[(

a(r−1,c) > 0)? (−I(r, c)) : (+I(r − 1, c))

]+ a(r,c) ·

[(a(r,c) > 0

)? (+I(r + 1, c)) : (−I(r, c))

]+ b(r,c−1) ·

[(b(r,c−1) > 0

)? (−I(r, c)) : (+I(r, c− 1))

]+ b(r,c) ·

[(b(r,c) > 0

)? (+I(r, c+ 1)) : (−I(r, c))

]. (6.38)

An example of the results this transformation may produce is shown in figure 6.29,

which utilizes the same data sets for the reference flat-field image and the image

to be distortion corrected as was used to produce figure 6.28.

6.7 Radiation Tolerance

As was discussed in section 2.3, integrated circuits are susceptible to degradation

when exposed to x-ray radiation. Because the signal processing electronics of

the Mixed–Mode PAD pixel lie in the beam path, directly behind the detector

diode, they will be subject to levels of radiation that will often exceed, during

a single experiment, the lifetime dose of most terrestrial electronics, by many

orders of magnitude. Consequently, the Mixed–Mode PAD was designed with

221

radiation tolerance in mind, as was detailed during our review of the pixel design

in chapter 4. Yet, since the most effective means of radiation hardening involve

component layout techniques that incur a substantial cost in terms of the circuit

area they require, brute force hardening of the entire circuit through its layout

was not an option. Instead, it was necessary to assess the impact of radiation

damage on individual pixel components and, then, balance the need to harden

these component with the constraints of the pixel area, developing a design that

used a mixture of mitigation techniques to fit within the limited pixel area a circuit

that was sufficiently tolerant of radiation damage for long-term use at synchrotron

light sources.

This section presents an evaluation of the radiation tolerance of the Mixed–

Mode PAD pixel based on laboratory measurements on the bare ASIC (i.e. no

detector layer) and synchrotron measurements on the hybridized device. It should

be understood that these measurements focus on the radiation tolerance of the

pixels within the hybrid rather than the long term radiation hardness of the device

as a whole. In particular, they do not evaluate the radiation tolerance of support

structures on the periphery of the array. The reason for this is primarily prag-

matic, as an evaluation of the radiation tolerance of these peripheral elements is

much more involved and the fault mechanisms more global than the comparatively

isolated situation of individual pixels within the ASIC. Furthermore, the radiation

hardness of these elements is not as critical as that of the pixel as they can be

shielded by building appropriate masks into the camera housing.

6.7.1 Comments on Units and Dose

Evaluating the radiation hardness of a detector such as the Mixed–Mode PAD can

be confusing because of the nontrivial relation between the flux incident on the

222

imager and the total dose accumulated in radiation-sensitive areas of the device.

Typically, when discussing radiation tolerance, one speaks in terms of the Total

Ionizing Dose (TID), as defined by the energy absorbed per unit mass of the

absorber,19 absorbed by the detector or a portion there of. Most often the reference

selected for these TID calculations is a portion of the detector that is particularly

sensitive to radiation effects. The problem with this approach is that it does

not make clear the relationship between this dose and the ultimately important

scientific quantity, the integrated flux on the surface of the detector. To illustrate

this point, consider that phosphor coupled CCD systems, discussed in chapter 2,

are rarely investigated for their radiation tolerance, although CCDs are known to

be susceptible to a variety of radiation damage mechanism, very similar to those

that affect PADs [62]. The reason for this is that the phosphor and fiber optic

effectively shield the CCD from damage by the x-ray beam, reducing the question

of radiation tolerance in the CCD itself to an academic exercise. Similarly, in

considering the radiation tolerance of a PAD detector it is not enough to only

speak in terms of the effect that a given dose of radiation has on a region of the

device. The relationship between this dose and the integrated flux on the surface

of the detector must be clear for the dose to have meaning.

As discussed in section 2.3, the dominant effects of radiation damage within

the ASIC layer of the hybrid are due to x-rays absorbed within the oxide layer. To

relate this to experimental quantities, i.e. the scattered intensity in a diffraction

peak, the shielding from the material within the diode layer must also be consid-

ered. As was also discussed in section 2.3, the absorbed fraction of x-rays follows

an exponential decay with path length through a material. For the 500 μm Si

19Traditionally, the absorbed does has been quoted in the unit of rad; however, continuationof this practice is discouraged in favor of the SI unit, the Gray: 1 [Gy] = 1 [J] / 1 [kg] [98]. Wewill adopt the SI standard in this thesis. Fortunately, conversion between the Gray and rad isnot difficult as 1 [Gy] = 100 [rad].

223

Con

tinuou

sE

xpos

ure

[s]

Energy [keV]

Φ = 108 [x−raysmm2-s

]

Φ = 106 [x−raysmm2-s

]

Φ = 104 [x−raysmm2-s

]

5 10 15 20104

106

108

Figure 6.30: Estimation of the continuous exposure times required for a total doseof 1 kGy(SiO2) for this Mixed–Mode PAD for three different flux densities incidenton the detector. These times are as calculated based on equation 6.39 assumingthat the flux density (Φ) incident on the detector is attenuated by 500 μm of silicon(the depth the Mixed–Mode PAD diode layer). Notably, these estimates do notinclude the additional protection the ASIC layer receives from the bump bonds.

detector diode used in the Mixed–Mode PAD, this means that the incident flux

(Φ) is attenuated by a factor of exp(−500[μm]

λSi(Ex)

), where λSi(Ex) is the attenuation

length in silicon at the x-ray energy Ex, as given by figure 2.5. With the atten-

uated flux after the diode (Φdio), we may estimate the TID in the SiO2 layer of

the ASIC.20 Since the depth of the SiO2 is small (5–7 nm for gate oxides and on

the order of 100 nm for field oxides) relative to attenuation length of x-rays within

the design range of the Mixed–Mode PAD (on the order of 10 to 100 μm), we may

use the small x approximation of the exponential (exp(−x) ≈ 1/x) allowing us to

remove the depth dependence from the absorbed dose through cancellation with

the depth term in the mass factor. It is then possible to derive the TID in the

20This estimate offers an upper bound, as it neglects the absorption from the metal inter-connect layers and bump bond that separate the diode from the Si surface of the ASIC. Themetal interconnect layers are extremely thin and composed of weakly absorbing Al interconnectsor SiO2 passivation, so we may consider them to be effectively transparent. The bump bondoffers significantly more protection, however, only to a limited portion of each pixel; hence, thiscalculation will express the TID expected in areas that it does not shield.

224

oxide independent of its thickness

TID(SiO2) = ΦdioEx

λSiO2(Ex) · ρSiO2

, (6.39)

where λSiO2(Ex) is the energy dependent attenuation length and ρSiO2 is the density

of SiO2 (∼ 2.2×103 kg/m3). Combining these allows us to calculate a TID related

to an integrated flux on the surface of the detector. This is expressed in figure

6.30, which shows, against axes of continuous exposure time and x-ray energy at

different flux levels, the contours of 1 kGy(SiO2) total absorbed dose.

6.7.2 Bare ASIC Damage

TID measurements were performed on bare, i.e. unhybridized, ASICs from the

AE190 submission,21 16×128 pixel test chip, and AE207 submission, final 128×128

pixel chip.

For the AE190 ASIC, dosing was performed at room temperature on inactive

devices that were removed from the dosing mount and tested at a probe station

in stages as dosing progressed. The x-ray source used was an Enraf Nonius X-Ray

Generator22 located in the Gruner laboratory at Cornell University. This rotating

anode source is equipped with a Cu target and was operated with electron beam

settings of 40 kV and 60 mA. An Osmic confocal multi-layer mirror23 was used

to collimate and monochromize the beam at the Cu Kα line (8.05 keV). The

flux was measured to be 4.9 × 107 x-rays/s/mm2, corresponding to a dose rate,

integrated over the beam area, of 0.216 Gy(SiO2)/s. In these measurements, no

signs of failures within digital pixel elements were seen up to 10 kGy(SiO2) TID.

Within the analog circuitry, a decrease in the number of digital counts for fixed

21Measurements on the AE190 were performed by Lucas Koerner and are summarized in [57].22Model FR571 (Enraf Nonius/USA–Bohemia, NY).23Model CMF15-165Cu8 (Osmic–Troy, MI).

225

integration time was observed within the dosed area. This may be attributed to a

reduction in the current sourced by the test current source resulting from shifts in

the threshold voltage of the current mirror transistor in this circuit induced by the

ionizing damage (see section 4.3.1 for a description of this circuit). In addition,

the one-shot24 pulse duration and the voltage retention time of the sample and

hold circuit were investigated. The former increased as damage accumulated, in

accordance with expectations. The latter degraded as a result of increased leakage

through the CMOS switch separating the sampling amplifier from the sampling

capacitor (see section 4.3.3 for a description of this circuit). As a result of these

measurements, in subsequent submissions, all CMOS switches connected to charge

sensitive nodes were changed to utilize an enclosed layout architecture for their

nMOS component.

To verify that the radiation tolerance observed in the AE190 devices extended

to the final AE207 submission a series of TID measurements was performed on an

unhybridized AE207 ASIC. Dosing was performed on active devices maintained at

a temperature of -25 deg. C so that these measurements would be more represen-

tative of actual operating conditions. The x-ray source utilized was the Christine

beamline in the Gruner laboratory at Cornell University, which is fed by a Rigaku

rotating anode source.25 This source supplies a Ni filtered Cu spectra dominated

by the Cu Kα line at 8.05 keV with negligible bremsstrahlung and Kβ components.

The source was operated with beam settings of 40 kV and 50 mA. A small hole in

a lead mask (∼50 μm thick) was used to isolate the beam to a roughly 3× 5 pixel

region, providing an integrated flux of 21.6× 106 x-rays/s for a dose rate of 0.278

Gy(SiO2)/s.

24The predecessor of the gated oscillator from section 4.2.2.3. Operationally, this circuit isvery similar to the gated oscillator except that it could initiate only one charge removal cycle percomparator cycle.

25Model 4151C6 (Rigaku/USA–Danvers, MA).

226

Unlike measurements on the AE190 submission, it was observed that ∼100

Gy(SiO2) was sufficient to induce problems with the digital circuitry, evident ini-

tially in an inability to program the CSR in portions of the ASIC and ultimately, at

the ∼1 kGy(SiO2) level, in null digital data from the ASIC—evidence of a failure

within the in-pixel counter. In unbonded detectors, there is no efficient method of

reliably testing the front-end response without the CSR, thus it was not possible

to evaluate the condition of the analog circuit while this digital failure persisted.

Annealing the active ASIC overnight, within the camera housing under vacuum,

through use of the thermoelectric as a heat source to raise the hybrid to an ele-

vated temperatures of +35 deg. C to +42 deg. C removed the problems seen on the

digital system. Subsequent repetitions of the dosing and annealing cycles yielded

similar damage and recovery patterns.

Regarding the pixel analog front end, at intervals of ∼10 Gy(SiO2) during the

dosing and then again after low temperature annealing for ∼10–15 hrs, when it was

once again possible to program the CSR, the analog front-end was examined for

indications of damage to analog pixel elements. Apart from the expected decrease

in the test current, corresponding to shifts in the threshold voltage of the test

current source transistor, no degradation in other analog parameters, specifically

the charge removal response of the amplifier and the sample and hold retention

time, were detectable.

The initial component to fail, the CSR, was present with an identical layout in

both the AE190 and AE207 devices. The absence of digital failure in the AE190

devices relative to the AE207 is postulated to be due to a combination of the lower

temperatures (ΔT ≈ −50 deg. C) at which the AE207 devices were operated and

the fact that the AE190 devices were not biased during operation. The relation-

ship between ionizing dose, temperature, and the operating state of the device

227

is complicated, but not intractable. As discussed in section 2.3.2, the dominant

long term effect of radiation damage is the trapping of holes in the passivation

oxide. However, the situation is not as simple as the outline in that section might

suggest. A complete discussion, reviewing the topic in full nuance, requires an ex-

tensive multi-volume series [9, 10]. Here, we will offer only a focused look into the

topic of the transport, trapping, untrapping, and ultimate removal of holes within

the oxide, intended to explain the discrepancies between the TID measurements on

the AE190 and AE207 submissions as well as provide guidance for future radiation

tolerance assessments of PAD devices.

A key point that needs to be appreciated, although it is glossed over in many

discussions of oxide ionizing radiation damage, is that holes are not trapped at

creation but rather have a low, and temperature dependent, mobility.26 They

may therefore drift or diffuse, depending on the the local electric field conditions,

until they recombine, are caught at a trap site, or leave the oxide. In most cases,

the absence of free carriers in the oxide means that when recombination occurs

it is between initial electron–hole pairs created by the ionization event [16]. The

likelihood of this is, however, strongly dependent on the presence and strength of

electrical fields within the oxide [16]. As an illustrative example, studies done in

the late 1980s on the TID effects of 10 keV x-rays reported the following empirical

relationship between the oxide field strength (Eox) and the fractional hole yield

(fh) after short-time-scale recombination [23],

fh(Eox) =

(1.35

Eox

[MVcm

] + 1

)−0.9

. (6.40)

Thus, in an inactive device, where the oxide field is ∼0, the fractional hole yield

will be practically zero. In comparison, a 0.5 V gate voltage applied across a 5

nm thick oxide, yielding oxide fields of 10 MVcm

, increases the fractional hole yield

26Typically holes in SiO2 have a mobility of 1.6 × 10−5 cm2/V · s at room temperature ascompared with 20 cm2/V · s for electrons [16].

228

to 89%. Consequently, much greater TID levels are required to induce equivalent

levels of damage in inactive, relative to active, devices.

Compounding the problem for nMOS devices is the issue that, when the de-

tector is operating, gate bias and channel current generate electrical fields in the

oxide that direct the drift of holes towards the channel [72]. This situation presents

three possibilities: either the hole will be trapped in a bulk trap, it will reach the

Si/SiO2 interface and become trapped in an interface trap, or it will enter the Si

and recombine with a electron supplied by the channel.27 As trap sites are typi-

cally due to oxide defects28 the cross section for trapping in the bulk is strongly

dependent on the quality of the oxide. However, even within very high quality

oxides with low bulk trap densities a substantial concentration of traps will occur

at the Si/SiO2 interface as a result of mismatching lattice parameters in the two

materials—which, incidentally, is also the location where trapped holes will have

the greatest effect on the channel. Thus active nMOS devices exhibit dual effects

related to electrical fields in their passivation, increased hole yield and a distribu-

tion of trapped holes biased towards the channel, that amplify the rate of device

degradation with total ionizing dose.

Cooling the detector also contributes to long term TID effects in MOS devices.

Initially this comes via decreased mobility in the charge carriers. To a limited

extent cooling will suppress the ionization yield fraction by making recombination

more likely. The significance of this is, however, highly dependent on the presence

of electrical fields in the oxide, as outlined above. Generally more significant is

that, with decreasing mobility, the the time a hole spends drifting through the SiO2,

27One may wonder what happened to the accompanying electron. While it is possible thatit could also be trapped in the oxide, the cross section for this is typically two to three ordersof magnitude smaller than that for holes. As a result most treatments ignore electrons in theirradiation portion of the TID assessment [16].

28A veritable menagerie of oxide defects exist, many too many to go into here. Those interestedin details on oxide defects are referred to [62].

229

before reaching the Si channel, is increased, thereby increasing the likelihood that

the hole will become trapped.

Figure 6.31: Illustration of TID recovery mechanisms for SiO2 adjacent to thechannel of an nMOS or parasitic nMOS device. The two dominant radiationdamage recovery mechanisms are tunneling, in which holes tunnel directly throughthe SiO2 into Si and as such is strongly dependent on the distance between thetrap and the channel, and the thermal emission, in which holes are thermallyemitted from low energy traps into the valance band of the SiO2 and drift towardsthe channel under the influence of fields in the oxide (assuming an active device).Adapted from [68].

From another perspective cooling the detector increases the TID effects by

depressing the rate at which holes are able to escape the oxide. Radiation damage

recovery is typically modeled as having two primary components, illustrated in

figure 6.31, one due to tunneling of trapped holes through the oxide and a second

due to thermionic emission of holes from traps into the SiO2 valance band and

subsequent drift or diffusion to the channel or gate where recombination may

occur. Tunneling through the oxide is strongly dependent on the separation of

the trap from the channel and to a lesser degree the electric field in the oxide

with only a very weak dependence on temperature [68]. Thermal emission, on the

other hand, is strongly dependent on temperature. This has been found to be well

modeled by an Arrhenius process with a second order pre-exponential factor; in

230

other words, a process with a rate constant (Rthm) governed by an equation of the

form

Rthm ∝ T 2 exp

{−Etrp

kT

}, (6.41)

where Etrp is the energy barrier required to tunnel into the oxide [8]. Without

detailed and difficult studies of the oxide to determine the distribution and energy

levels of the trap states, it is not possible to predict the fractional importance of

these effects, except perhaps in the limiting case of very thin gate oxides where one

expects recombination through tunneling to dominate at reasonable temperatures.

However, these considerations offer a compelling explanation of why digital failures

were seen at the relatively low dose of 100 Gy(SiO2) in a cooled and active ASIC

while the same structures showed no damage when dosed up to 10 kGy(SiO2) in

an inactive, room temperature device.

Device recovery following annealing is expected based on detailed, transistor-

level studies of TID effects on deep sub-micron technologies [3, 58, 59, 28]. These

studies have shown that, at the transistor level, damage from TID levels of > 10

kGy(SiO2) may be recovered from through annealing at temperatures of 100 deg.

C over 10 to 15 hours. Our work indicates that the 100 Gy(SiO2) damage threshold

of the Mixed–Mode PAD may be recovered from on similar time scales and at lower

temperatures (∼40 deg. C) that are straightforward to obtain within the detector

housing by using the camera thermoelectric as a heat source rather than a heat

sink. The vacuum environment of the cryostat is advantageous in this regard as it

prevents degradation of the oxide through hydrogen binding during the annealing

process. Because of this, regular low temperature annealing is not expected to

damage the detectors.

This work, however, indicates that a part of the regular operating procedure of

a Mixed–Mode PAD camera should entail a period wherein the temperature of the

231

detector hybrids should be raised while the hybrid is active and time allowed to

remove damage. If low-temperature annealed overnight, once a week, it is unlikely

that damage will accumulate to appreciable levels. In the event of more significant

damage, e.g. if a beam stop were to fall off and the detector were to be exposed to

the main beam for an extended period of time, this too should be recoverable in

a short period of time by further elevating the detector temperature (e.g. to 100

deg. C).

6.7.3 Hybridized ASIC Damage

While the Cu targets of the rotating anode sources within the Gruner lab are an

effective means to deliver dose to the oxide of a bare ASIC, figure 6.30 reminds

us how much longer their predominantly 8.05 keV beams, whose flux is on the

order of 107 x-rays per second, will take to deliver a similar dose to the oxide of a

hybridized detector. At a synchrotron light source, though, one is not restricted to

characteristic emission lines and flux intensities are three to six orders of magnitude

higher, offering a much more practical means to massively irradiate hybridized

detectors.

Tests in April of 2007, at the CHESS F2 beamline, a description of which will

be given in section 7.4.3.1, systematically examined dosing of a Mixed–Mode PAD

hybrid by placing various regions of the imager into the unattenuated, monochro-

matic 13 keV main beam for extended periods of time. The particular hybrid cho-

sen for this experiment was a defective device, due to unconnected bump bonds

and scratches on the surface that generated excess leakage current, the most in-

triguing of which resembled the letters “W4.”29 The ASIC, however, was perfectly

29Early in the fabrication of the first large-area hybrids, one of our collaborators scribed waferidentifiers onto a few detector diodes in an attempt to make inventory management easier. Hencethe ‘W4’ indicates that the detector layer for this hybrid came from wafer #4. Needless to say,this practice was halted shortly after the first hybrids were tested.

232

[mm]

[mm

]

-5 0 5

-5

0

5

(a) Background

[mm]

[mm

]

-5 0 5

-5

0

5

(b) Exposure

[mm]

[mm

]

-5 0 5

-5

0

5

(c) Difference Image

Figure 6.32: Silver Behenate diffraction (neg.) from a hybrid used in theSynchrotron-based radiation-tolerance experiment. Panel (a) shows a combina-tion of ten 1 s background images. Panel (b) shows a combination of ten 1 sexposures of a Silver Behenate powder sample, with no beam stop. The differenceof panels (a) and (b) is shown in panel (c), where the intensity scale of the differ-ence image is an order of magnitude smaller than that used in the exposure andbackground images. The radiation induced damage to the diode can be seen bythe 10 large (∼1 mm2) spots of greater intensity in the background and exposureimages, two in a column in the upper left quadrant of the image and eight in twocolumns of four spots in the upper right quadrant of the imager. From left to right,by column of damage locations, the exposure times were: (first column) 1440 s,1920 s; (second column) 360 s, 30 s, 720 s, 960 s; and (third column) 60 s, 120 s,240 s, 480 s.

233

functional and defects mentioned were isolated to specific regions of the hybrid.

Using the defect free regions, a total of 10 doses were taken with exposure times

of varying from 0.5 minutes to 32 minutes. The total flux on within the beam was

monitored using the CHESS standard Ishort ion chamber, placed immediately in

front of the detector. As the beam profile and, hence, the dosing profile were not

flat, images of the beam taken with a 2.3 mm Al absorber to estimate the beam

profile.

I lgk,d

am/I

lkg,c

ln

Time In Direct Beam [s]0 500 1000 1500 2000

0

2

4

6

8

(a) Time In Beam

I lgk,d

am/I

lkg,c

ln

TID [kGy(SiO2)]0 100 200 300 400

0

1

2

3

4

5

6

7

(b) Estimated TID

Figure 6.33: Fractional leakage increase in primary beam region as a function oftime in the main, uncollimated, F2 beam, panel (a), and estimated TID, panel (b).In the estimated TID plot, the point corresponding to 960 s was removed due tosuspected beam fluctuations, as discussed in the text.

Analysis of the effects this dose has on the pixel is complicated by the fact that

it is difficult to accurately estimate the total dose acquired by particular portions

of the detector. This is a consequence of drift in the beam, both in terms of

total intensity and spatial intensity distribution, on long time scales. The drift

in beam intensity and profile were expected and measures were taken to mitigate

it; specifically, the total intensity was monitored by the by chamber mentioned

previously and images of the beam profile were taken between exposures.

234

Beam intensity fluctuations are somewhat mitigated by the design of the F2

beamline. Typically, the intensity of a synchrotron beamline decays over the du-

ration of a fill (i.e. the period in which a single group of electrons or positrons is

held in the storage ring) due to a gradual loss of beam current. The F2 beamline

incorporates a feedback mechanism to minimize this effect, practically de-tuning

the beamline at the start of the run and tuning it up as the run progresses, so that

the beam intensity is maintained as constant as possible over the full duration of

the run. As a result, the variations in beam intensity were less than 10% from the

start to the end of this data set.

The impact of fluctuations in the beam profile was more insidious in this regard,

as there is no easy way to monitor it while the dosing is occurring and the impact of

this damage exhibits a nonlinear response. This point is illustrated by the aberrant

960 s data point in panel (a) of figure 6.33. The raw leakage in the peak region

of this portion of the device was substantially higher than that exhibited by other

elements, even those receiving significantly greater dose. As the damage profile of

this spot also differs significantly from those of the other spots, it is likely that

the beam was less stable during this exposure, providing greater damage to pixels

neighboring the peak; a consequence of the nonlinear leakage increases with TID

exhibited in figure 6.33.

Despite the increased leakage, the defect-free regions of the detector are usable

for imaging. This is illustrated by the Silver Behenate powder diffraction pattern

shown in panel (c) of figure 6.32. This data was taken on the Christine rotating

anode beamline at the Gruner lab. For this measurement, the x-ray generator

was operated at 40 kV and 50 mA. To produce this image, the sum of ten 1

s backgrounds, shown in panel (b) of figure 6.32 was subtracted from ten 1 s

exposures, shown in panel (a) of figure 6.32, with the hybrid operated at -25 deg.

235

C. Despite the fact that the leakage was substantially stronger than the scattered

x-ray signal, it has significantly cleaner statistics, as was discussed in section 6.1,

that allowed it to be removed through background subtraction, without appreciably

distorting the desired signal.

6.7.4 Conclusions on Radiation Tolerance

Based on our radiation tolerance assessments, the digital circuits in the Mixed–

Mode PAD, specifically the CSR and the counter, show susceptibility to radiation

damage near 100 Gy(SiO2) TID. No degradation can be seen in the analog response

up to this level, nor at any post-annealing level where the CSR functions.

The damage to the digital electronics is first apparent in the CSR due to the

smaller transistor widths (at minimum length) used in its structures, compared

to those in counter. By design, however, damage to this circuit does not degrade

the performance of the pixel. This failure point is therefore quite useful as it

allows the CSR to act as a “miner’s canary” indicating, through an inability to

program past the damaged area, when radiation damage has reached a level that

the functionality of the pixel is itself at risk.

That said, there is no reason that this failure should ever be observed during

normal operation of the Mixed–Mode PAD. This is because the level of radiation

damage at which problems in the digital circuitry become apparent is quite high,

with 100 Gy(SiO2) representing nearly 83 continuous hours in a 13 keV beam with

a flux of 106 x-rays/mm2/s or more than 8,000 hours at the same flux in a 8.05 keV

beam. This level of flux is much higher than what one expects from all but the

brightest spots in a conventional scattering experiment. Consequently, one could

expect months of operation before any failures would become evident on the digital

system and therefore, a regular (weekly or biweekly), overnight, low-temperature

236

anneal should prevent the accumulation of damage from ever reaching a level where

it may be observed.

6.8 Conclusions

Before attempting to use an imager like the Mixed–Mode PAD in scientific experi-

ments, it is essential to gain a sufficient understanding of the device to confidently

interpret the images it produces. In this chapter, we have delved into the details

of the Mixed–Mode PADs performance, striving to offer a characterization of the

detector that meets these ends.

Our investigations began with individual pixels, demonstrating their basic lin-

earity, when the correct scaling between the analog and digital data is used, and

was followed by a discussion of the read noise that showed that single x-ray sen-

sitivity could be expected over a wide range of exposure times. From individual

pixels, we moved to the imaging properties of the device as a whole, first consid-

ering the collection of charge from the diode layer and noting how the profile of

measured signal was strongly dependent on the detector diode bias but the total

signal collected was not. Our focus then moved to a careful analysis of the ensem-

ble mean spatial response of the detector, both in the analog limit and considering

the effects of pixelation on the device. From here, we concluded our investigation

of the imaging properties of the detector with an examination of the causes and

effects of spatial distortions within the device. Having looked at individual pixels

as well as the imager as a whole, we used a measurement of the Detector Quantum

Efficiency to predict the sensitivity of the uncalibrated imager. Here a conscien-

tious effort was made not to make claims about attainable sensitivity, just what

one could expect from a 0th order device.30 Instead, a discussion was presented

30This was done because measurements of the sensitivity of a tuned detector would only reflect

237

reviewing how the instrument can be calibrated and corrected to improve upon

the sensitivity of the uncalibrated imager. Finally, the radiation tolerance of the

device was assessed and found to be acceptable.

the effort put in to characterizing a particular device and as such would not be representativeof what could be generally expected from the imager—though, there is a good chance that theywould be enshrined as “typical performance” in future detector literature.

238

CHAPTER 7

FIRST MIXED–MODE PAD EXPERIMENTS

The first experiments with the Mixed Mode PAD that are presented here can

be divided between those intended to demonstrate particular characteristics of

the Mixed–Mode PAD and those intended to highlight fields where we believe

the Mixed–Mode PAD has the potential make a significant scientific contribution.

In the former category, we present three experiments that illustrate, respectively,

the sensitivity, well depth, and spatial resolution of the Mixed–Mode PAD. In

the later category, we strive to illustrate the scientific impact a detector like the

Mixed–Mode PAD can be expected to have through actual experiments. To this

end, studies were conducted of protein diffraction and self assembly of atomically

thin monolayer films. This work is limited in scope by the relatively small active

area of the single module prototype camera and the reasonable tenure of a graduate

student. Still, it serves to illustrate the potential a full-sized, 512 × 512 pixel or

larger for crystallography, or 128× 512 pixel or larger for surface studies, has for

these fields. Despite these limitations the prototype Mixed–Mode PAD camera

was able to acquire data sets that would have been very difficult, if not impossible,

to take with competing x-ray imaging technologies.

7.1 Spectral Lines

One of the touted performance characteristics of the Mixed–Mode PAD is its wide

dynamic range, which we have claimed extends from single x-ray sensitivity, at

least for 10 keV x-rays, to a full well depth of more than 2 × 107 10 keV x-rays.

To demonstrate the capacity of the Mixed–Mode PAD to measure very weak x-ray

signals, we performed a series of experiments where a single pixel was illuminated

with x-rays, predominantly of one characteristic energy, and then taking multiple

239

−20 0 20 40 600

1000

2000

3000

4000

5000

6000

[N]

[mV]

Figure 7.1: Observed spectrum from 1 ms exposures of a single pixel within theMixed–Mode PAD, operating at -35 deg. C, illuminated by an unfiltered Cu x-ray tube operated at a bias of 25 kV and 0.4 mA of tube current. A 75 μmpinhole mask was used to isolate the x-ray beam to the interior of the pixel sothat charge sharing effects were negligible. The spectrum of the Cu source willbe dominated by the Cu Kα characteristic emission line. However, there will alsobe a significant bremsstrahlung component extending up to the tube bias voltageof 25 keV. Because of this, it is very difficult to distinguish quantized Kα peaksbeyond 0, 1, and 2 x-rays.

short exposures to build a histogram of the distribution of x-ray induced signal,

i.e. an observed spectrum.1 The goal in these experiments was to show that the

sensitivity of the Mixed–Mode PAD made it possible to observe quantized aspects

of predominantly monochromatic source spectra.

To see how this works, note that if the source spectrum is given by Φ(Ex), where

Φ(Ex) is the x-ray flux at energy Ex, then the likelihood (P (Ex, n)) of observing n

x-rays of energy Ex within an exposure of duration texp, assuming a Poisson source,

is given by

P (Ex, n) =(Φ(Ex) · texp)

n exp (−Φ(Ex) · texp)

n!. (7.1)

1Note that, since we are using an integrating device, the observed spectrum for an integrationof a given duration is not equivalent to the source spectrum but a derivative thereof.

240

Now, suppose that a large number of constant duration exposures are taken. Each

exposure will contain a number of x-rays of varying energy. We are interested in

the probability that the sum of the energy of these x-rays (P (Edep)) will be a given

energy (Edep), as knowing P (Edep) for all possible Edep is equivalent to knowing our

observed spectrum. If we let {Ex, n} describe the results of a given measurement,

where one reads this as the set of x-ray energies (Ex) within the source spectrum

and their respective observed occupancies (n) during a particular measurement,

then the probability of this result occurring is given by

P ({Ex, n}) =∏{Ex,n}

P (Ex, n). (7.2)

The total energy deposited in the detector by {Ex, n} is then

Edep({Ex, n}) =∑{Ex,n}

n · Ex. (7.3)

This, then, gives us the machinery to describe the spectrum of results that we

expect to measure from a pixel within the Mixed-Mode PAD as

P (Edep) =∑

({Ex,n}|Edep({Ex,n})=Edep)

P ({Ex, n}). (7.4)

The complexity of this final form is indicative of how difficult it can be to observe

aspects of the source spectrum by looking at integrated quantities rather than

individual x-rays, particularly when the source contains a complicated spectrum

or there are effects like charge sharing at pixel boundaries. However, as figure

7.1 illustrates, even with the relatively complicated spectra from an unfiltered Cu

x-ray tube,2 it is possible to distinguish elements of the source spectrum when

texp is sufficiently short. With simpler source spectrum, e.g. those with only a

single characteristic line, limited background radiation, and where care is taken to

mitigate charge sharing effects, still more quantized aspects of the source spectrum

may be observed.

2Model TFS-6050Cu with power supply TCM-5000M (Trufocus–Watsonville, CA).

241

Vres [mV]

[N]

-10 0 10 20 30 400

500

1000

1500

2000

2500

(a) texp = 1 ms

Vres [mV]

[N]

-10 0 10 20 30 400

500

1000

1500

2000

2500

(b) texp = 2 ms

Vres [mV]

[N]

-10 0 10 20 30 400

500

1000

1500

2000

2500

(c) texp = 4 ms

Vres [mV]

[N]

-10 0 10 20 30 400

500

1000

1500

2000

2500

(d) texp = 6 ms

Figure 7.2: Spectra of the acquired signal from a series of short exposures withMolybdenum x-ray tube, operated at 30 kV with 0.4 mA tube current and attenu-ated by a 791 μm Al absorber, collimated with a 75 μm pinhole mask to restrict thebeam to the interior of a single pixel, thereby eliminating charge sharing effects.

242

The first real attempt to measure multiple quantized x-ray peaks utilized a Mo

x-ray tube3 operated at a bias of 30 kV with 0.4 mA tube current. A 791 μm

Al absorber was used to remove low-energy bremsstrahlung radiation, leaving a

spectrum dominated by the Mo Kα characteristic emission line at 17.5 keV. With

the detector at -35 deg. C, short integrations were used to limit the number of

x-rays observed to 0, 1, 2, or (rarely) 3. To eliminate charge sharing effects, a 75

μm mask was used to isolate the incident flux onto a single pixel within the array.

A large number, ∼10,000, exposures were then taken in this manner to produce

the four spectra shown in figure 7.2. These spectra show clear peaks at 0 keV,

17.5 keV, and suggest peaks at 35 keV and 52.5 keV. Due to the presence of other

x-ray energies within beam, specifically bremsstrahlung radiation above 10 keV

that was not effectively removed by the Al absorber, the high energy peaks are

notably blurred.

To improve this measurement, an essentially monochromatic source was em-

ployed. This source was derived from a Cu rotating anode4 operated at 40 kV and

60 mA with multilayer optic5 to isolate the Cu Kα line at 8.05 keV. In addition, a

50 μm thick Ni filter was used to reduce the intensity of the monochromatic beam

and physically support a 50 μm thick Tungsten (W) mask with a 1 mm × 1 mm

grid of 25 μm holes. By aligning a hole illuminated by the x-ray beam with a pixel

in the imager, it was possible to completely isolate the x-ray signal to that single

pixel. For a monochromatic source with no charge sharing, equation 7.4 then re-

duces to the basic Poisson distribution of equation 7.1, with the caveat that each

peak is broadened by the read noise of the detector. In this experiment, it was then

possible to observe a large number of x-rays without substantial blurring of the

quantized x-ray peaks, as demonstrated by panel (a) of figure 7.3. Panel (b) of the

3Model TFS-6050Mo with power supply TCM-5000M (Trufocus–Watsonville, CA).4Model FR571 (Enraf Nonius/USA–Bohemia, NY).5Model CMF15-165Cu8 (Osmic–Troy, MI).

243

Vout [mV]

[N]

0 20 40 60 80 1000

100

200

300

400

(a) Observed Spectra

Vout [mV]

[N]

0 20 40 60 80 1000

100

200

300

400

(b) Observed Spectra with Fit

Figure 7.3: Observed Poisson spectra for 1 ms integrations from a Cu rotatinganode source, monochromatized at the Cu Kα line at 8.05 keV. A 25 μm pinholemask was used to isolate the x-ray signal to the interior of a single pixel, thuspreventing charge sharing. Panel (a) depicts the observed spectra, panel (b) showsthe same result along with a three-parameter fit, where the scaling of the peakseparation, the common width of each Gaussian peak, and the location of the zerox-ray peak are allowed to vary and be optimized.

244

same figure shows a fit to this data in which the scaling of the peak separation, the

common width of each Gaussian peak, and the location of the zero x-ray peak are

allowed to vary and optimized. Given the limited degrees of freedom, the quality

of the resulting fit is quite good, with a reduced χ-squared error of 0.9. One very

important consequence of this measurement is that it provides an exceptional tool

for determining characteristics of the pixel, such as the pixel gain and the detector

read noise, to an accuracy of better than a fraction of a percent.

It is noteworthy the there are very few x-ray imagers that are capable of produc-

ing an observed spectrum like that shown in figure 7.3. The fine spectral resolution

evident in this figure is a result, not only of the low noise of the Mixed–Mode PAD

front-end electronics, but of the merits of direct x-ray detection. As discussed in

section 2.3, direct detection of x-rays is a Fano limited process yielding better than

Poisson statistic in terms of photocurrent generation. Consequently, phosphor cou-

pled CCDs, even with their lower read noise, would not be able to produce a figure

like this due to their much larger uncertainty in signal yield that the indirect x-ray

detection method, used by these imagers, introduces. It also goes without saying

that a photon-counting PAD could not produce this spectra due to the information

lost by photon discrimination. In purely analog PADs, there is a split due to the

trade off between gain and total well depth such that analog PADs designed for

sensitivity, e.g. the PAD being developed for the single-protein diffraction experi-

ments [76], are capable of measurements with this level of sensitivity while deeper

well depth devices, e.g. the Cornell 100×92 PAD [83], are not. No other analog

PAD combines this level of sensitivity with the total well depth offered by the

Mixed–Mode PAD.

245

7.2 Wide Angle Scattering From Sheet Aluminum

While diffraction from sheet aluminium may, at first glance, seem a rather benign

experiment, this simple measurement serves to concisely illustrate some very im-

pressive properties of the Mixed–Mode PAD—distinguishing it from other x-ray

imagers in use or in development. Recall that it is the combination of analog and

digital data in the Mixed–Mode PAD allows for a large total well-depth while simul-

taneously allowing a high maximum input flux per pixel. As discussed in chapter

4, the Mixed–Mode PAD combines 18-bits of digital data with the well-depth per

pixel of an analog charge collector. The well-depth of the analog collector is a

variable parameter that may be set within a range of ∼20 to ∼150 10 keV x-rays,

though typically the detector is operated with a setting equivalent to ∼100 10 keV

x-rays. This configuration yields a total system well-depth of more than 2.6×107

10 keV x-rays. The speed of the pixel circuitry is designed to allow a minimum

quantized charge removal rate of 1 MHz which corresponds to a maximum input

flux of at least 108 10 keV x-rays/pixel/s.

To succinctly demonstrate the performance of the Mixed–Mode PAD across a

broad range of signal levels and flux intensity a single, one second, exposure of

1/32th in (794 μm) sheet of rolled aluminium was taken, with no beamstop, us-

ing the collimated main beam from the Cornell High Energy Synchrotron Source

(CHESS) F2 beamline. The intensity of the x-ray beam on the sheet aluminium

was on the order of 1011 x-rays/mm2. This configuration produced extreme flux

conditions on the detector, near the limits of the Mixed–Mode PAD design spec-

ifications, as well as scattered x-ray intensities nearly five orders of magnitude

weaker. The resulting diffraction pattern is described in figure 7.4 with views of

the same image on four different intensity scales as well as cross-sectional line

profile.

246

(a) (b) (c) (d)

→ → Increasing Intensity Scale → →

Radial Distance [pixels]

X-r

ays/

pix

el

-80 -60 -40 -20 0 20 40 60 80102

104

106

108

(e) Line Profile Through Diffraction Center

Figure 7.4: A wide-angle diffraction data set from a thin aluminium sheet is shownat increasing intensity scales from image (a) to image (d). An angular profile of thisdata is shown in panel (e); note that the vertical axis is logarithmic. The data setwas acquired in a single, 1 s exposure and clearly illustrates the large dynamic rangeof the Mixed–Mode PAD. Both the signal of the attenuated main beam (shownin image (a) with a peak flux of 18 million x-rays/pixel/sec) and the sixth-orderring (shown just inside, though not at, the edge of images (c) and (d) or as the5th peak from the center in panel (e) with a peak flux of ∼700 x-rays/pixel/s) areclearly visible and measured with good statistics although they differ in intensityby a factor of more than 25,000. The dynamic range of the Mixed–Mode PAD is,in fact, larger than this example would suggest, as even fainter rings should alsobe observable with a larger-area Mixed–Mode PAD detector.

247

Consequently, this range of flux allowed us to measure, in a single exposure,

signal levels that spanned nearly the entire well-depth of the detector. In the

resulting diffraction pattern, shown in figure 7.4, the brightest pixel, located in

the transmitted image of the direct beam at the center of the pattern, recorded

more than 1.8×107 x-rays while in the sixth order diffraction ring, visible at the

highest level of magnification, the brightest pixel reports only ∼700 x-rays. The

intensities recorded by these two pixels differed by more than a factor of 25,000,

which notably is larger than one third of the total well-depth of typical phosphor-

coupled CCD x-ray detectors, and yet, as was demonstrated in section 7.1, the

sensitivity of the Mixed–Mode PAD extends well below the minimum presented

by this illumination pattern, indicating that with a larger area detector it should

be possible to see even fainter diffraction rings.

[mm]

[mm

]

-4 -2 0 2 4

-4

-2

0

2

4

(a) Scaled Diffraction Image

Nor

mal

ized

Inte

nsi

ty[x

-ray

s/pix

el]

Distance From Diffraction Center [mm]0 1 2

1000

1500

2000

2500

(b) Avg. Intensity vs Radius

Figure 7.5: Panel (a) shows a zoomed in region of the Al WAX image from figure7.4, scaled to more clearly display the diffraction from higher-order harmonicspassed through the monochromator. A quantitative description of this scatteringis show in panel (b), indicating an average intensity of 300 x-rays/pixel. Whatis remarkable about this image is that it is possible to see such a weak signal sonear to the much more intense transmitted main beam and primary first-orderdiffraction ring.

Another remarkable feature about this image, illustrating a consequence of

248

the sub-pixel impulse response of these detectors, is shown in figure 7.5. Here,

a comparably faint diffraction ring, presumably from a higher-order harmonic of

the beam, is evident; encircling the transmitted main beam at a distance of ∼1.3

mm from the diffraction center, roughly one half the distance of the primary first

order diffraction ring. That this signal is visible so near to the transmitted beam

and primary first order diffraction ring, whose maximum intensity per pixel are,

respectively, roughly five and two orders of magnitude larger, is a testament to the

fact that the spatial spread signal from any x-ray is limited to, at most, nearest-

neighbor pixels. Thus, even if one had a phosphor coupled CCD system that had

sufficient well depth to record this diffraction image, the tails in its point spread

function would prohibit observation of this feature.

7.3 Fine-sampled Image Resolution

As discussed extensively in section 6.4, the spatial response of the Mixed–Mode

PAD is dominated by the detector pixelation. For diffraction experiments this

is typically not an issue as the diffraction spot or ring, as in the case of powder

diffraction or small angle scattering, normally extends over a region of pixels with

spot or ring separations greater than the pixel spacing. In these measurements one

is typically interested in the total signal in the peak or ring as well as the mean

location of the scattering, so the detailed spatial response is typically not a con-

cern. However, this effect must be considered for radiographic or other continuous

imaging experiments.

To demonstrate the spatial distortion effect we begin by looking at a single

radiographic image, shown if figure 7.6. This image is of a Canadian dime whose

head side was filed away to avoid superposition of two images. It was produced by

using the dime to occult the unattenuated flood field produced by a Molybdenum

249

[mm]

[mm

]

-8 -6 -4 -2 0 2 4 6 8

-8

-6

-4

-2

0

2

4

6

8

Figure 7.6: Single radiographic image of a Canadian dime taken with a Mo x-raytube biased at 30 keV. The opposing face of the coin was filed off to provide aclearer image and increase transmission.

250

[mm]

[mm

]

-8 -6 -4 -2 0 2 4 6 8

-8

-6

-4

-2

0

2

4

6

8

Figure 7.7: Fine–sampled radiographic image of a Canadian dime taken with a Mox-ray tube biased at 30 keV. The opposing face of the coin was filed off to providea clearer image and increase transmission.

251

x-ray tube6, biased at 30 kV with 0.4 mA of tube current, after a ∼1 m air filled

flight tube. The exposure duration was 1 s and 25 background subtracted images

were combined to produce the image shown. As expected based on the discussion

in section 6.4, the effects of pixelation are most evident along boundaries, where

the local spatial frequencies are highest,7 such as the edges of the sail, the rigging,

the dots that border the interior of the coin edge, and the coin edge itself.

With a little extra work though it is possible retrieve the frequencies lost to

aliasing, realizing the spatial response of the MTF shown in figure 6.19. To do

this we use a method similar to that employed in section 6.4 to study the spatial

response of the detector and recover information from spatial frequencies beyond

the detector Nyquist Limit. Specifically, by translating the detector in sub-pixel

steps it is possible approximate the pixel’s continuous spatial response. This is

shown in figure 7.7, which takes 100 single images, identical to figure 7.6, randomly

located relative to each other and merges their response with the filter discussed

in section 6.4.

To elucidate the difference between these images, zoomed regions of the jib sail

and coin edge are shown in figure 7.8, with direct comparison between the pixelated

and fine-sampled images. What is remarkable about these images is not only the

blockage the pixel size imposes on the image, but more so the fine resolution that

one is able to retrieve because of the sub-pixel analog impulse response of the

detector. In contrast, were an analogous set of images taken with a phosphor

coupled CCD, binned to offer similar sized pixels in terms of collection area in

the phosphor, one expects very little improvement with fine sampling due to the

substantially broader impulse response of the detector.

6Model TFS-6050Mo with power supply TCM-5000M (Trufocus–Watsonville, CA).7Local spatial frequencies are a concept from Wavelet Analysis. For more information see

[66].

252

[mm]

[mm

]

-4 -3 -2 -1 0

-5

-4

-3

-2

-1

0

(a) Sail, Single

[mm]

[mm

]

-4 -3 -2 -1 0

-5

-4

-3

-2

-1

0

(b) Sail, Fine–Sampled

[mm]

[mm

]

3 4 5

3

4

5

6

7

8

(c) Edge, Single

[mm]

[mm

]

3 4 5

3

4

5

6

7

8

(d) Edge, Fine–Sampled

Figure 7.8: Comparison of magnified regions of figures 7.6 and 7.7. Panels (a) and(c) show sections of the single radiographic image, a portion of the sailboat jib andthe right lower edge of the coin, selected to highlight the effects of pixelation onthe image. One dead pixel is evident by the black square in panel (a). Panels (b)and (d) show the same regions, respectively, fine–sampled to remove the pixelationeffects.

253

7.4 Protein Crystallography

The Mixed–Mode PAD project was funded by the National Institute of Health in

2003 to build an x-ray detector for Protein Crystallography possessing exceptional

characteristics not found in the generation of x-ray imagers available at synchrotron

beamlines. With this in mind, it is important that the inaugural synchrotron ex-

periment for the Mixed–Mode PAD should be collecting diffraction from a protein

crystal.

The usefulness of a single detector hybrid in this work is somewhat limited,

due to its small active area—for comparison, the typical phosphor-coupled CCD

system used on a crystallography beamline will have over 100× the active area of

a single Mixed–Mode PAD detector hybrid. For this reason, the results presented

in this section do not focus on the bread and butter work of most protein crys-

tallographers, solving protein structures, but instead look towards new techniques

and experiment possibilities that unique features of the Mixed–Mode PAD bring

to this field.

7.4.1 Overview of Protein Crystallography

For a crystal diffraction experiment, a narrow collimated beam of x-rays is used

to illuminate a crystalline sample. While the majority of the primary beam is

transmitted through of the crystal, a fraction interacts with the electrons bound

to each atom and are, as a result, scattered in different directions. If the scattering

elements are localized in a structure and these structures are, in turn, arranged in

a periodic two- or three-dimensional array, then portions of the scattered radiation

may interfere constructively to produce pronounced beams of x-ray intensity [6, 1],

whose locations are in accordance with Bragg’s Law. A full derivation of x-ray

scattering formulas is the proper subject of an extended text, such as the two

254

preceeding references or [79]. For our purposes though, the primary result from

these sources is that the diffraction reveals a portion of the Fourier Transform of

the electron density map of the crystal, i.e. a portion of the reciprocal space of the

crystal. The goal of crystallography is to use diffraction to determine a sufficient

portion of the crystal’s reciprocal space to reconstruct the electron density map of

the basic element of the crystal lattice, the unit cell. From this, then, the atomic

structure of the crystal may be derived.

Figure 7.9: Image of the Thaumatin protein crystal used for the diffraction exper-iments reported in this section.

While this description holds for all forms of crystallography, there are a num-

ber of points that distinguish the challenges of Protein Crystallography. Foremost

among these is the complexity of the diffraction patterns produced by macro-

molecular biological molecules. A direct result of the complexity of the protein

molecules, and, thus, their electron density maps, is that the diffraction patterns

have hundreds to thousands of unique peaks, as the image of a diffraction pattern

from a Thaumatin protein crystal shown in figure 7.10 illustrates. Consequently,

to obtain sufficient information about the diffraction to reconstruct the electron

density map of the protein molecule a substantial portion of the crystal’s recip-

rocal space must be mapped out through rotation of the crystal relative to the

255

Figure 7.10: Mosaic image of the diffraction pattern from the Thaumatin proteincrystal shown figure 7.9, when rotated through Δφ = 1 deg. in 1 s. This imagewas made by combining sixteen separate images (i.e. tiles) of the same crystalrotation, acquired with the same single PAD hybrid at sixteen different detectordisplacements. In each tile a separate background image was subtracted and thetiles global scaling was adjusted to offset beam intensity variation. The borderevident at the edge of each tile is due to a one pixel overlap region between images.The data in this edge region is of poor quality due to the high edge leakage of theuncooled detector. This was the first protein diffraction pattern taken with theMixed–Mode PAD. The image is shown to scale.

256

incident x-ray beam. The exact number of images this requires will depend on the

quality of the crystal, the complexity of the biological molecule, and symmetries in

the crystal structure; however, data sets containing hundreds of images are quite

common.

As an additional challenge faced by Protein Crystallographers, there are notable

differences between even a high-quality protein crystal and an ideal crystal. Large,

well-ordered protein crystals are difficult to produce because the large and irregular

shaped protein molecules do not pack into crystals without forming large void areas

and channels within the individual molecules [15]. As a result, the crystals used

for protein crystallography depart from the ideal crystal response of in two ways.

First they are rarely a single perfect crystal, but rather made up of many small

blocks randomly misaligned with respect to each other. In addition, as each block

has finite extent the diffraction spot from each block will have an intrinsic spread,

or rocking width, that is inversely proportional to the size of the crystallite. In this

“mosaic” model of a crystal, the intrinsic spreads of the separate crystal blocks

and the misalignment factors combine to give a width of each diffraction spot on

the order of 0.1 deg. [45].

For reasons that will be presented in more detail in the next section, the chal-

lenges presented by the large fraction of the crystal’s reciprocal space that needs to

be sampled and the mosaic spread of these diffraction spots places a strain on the

current generation of synchrotron x-ray images. The large-area, phosphor-coupled

CCDs typically used to acquire diffraction data sets at synchrotron beam lines are

pressed in terms of their frame rate and spatial resolution by the need to acquire

many images in as short a time as possible, in which the diffraction from individual

spots is well resolved from that of neighboring spots. For these reasons, as well

as others we will soon discuss, a new generation of PAD-based x-ray imagers is

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being developed, among which the Mixed–Mode PAD, for its integrating rather

than photon counting front end, stands out.

7.4.2 Data Collection–Towards Finely Slicing the φ

One area in which fast framing imagers like the Mixed–Mode PAD are expected

to have a dramatic impact is the way in which synchrotron data sets are taken.

To explain this, though, let us first review the canonical approach to acquiring a

protein crystallographic data set at a synchrotron source. An example of a protein

crystal is shown in panel (a) of figure 7.10. This crystal is mounted on a loop and

pin system with a magnetic base. The experimental stage used for performing the

diffraction measurement is described in figure 7.11. As this figure indicates, the

sample is mounted on the goniometer via magnetic attachment to the mounting

pin. While it is mounted in this apparatus, a steady stream of boil-off nitrogen is

used to keep the crystal frozen. This stream is supplied by a device known as a

coldstream, partially shown in figure 7.10 by the tube directly above the labeled

diffraction center, offers a controlled flow rate of temperature-maintained boil-

off nitrogen over the crystal to maintain the crystal temperature. Unless noted

otherwise this device was used to keep the crystal temperature at ∼100 deg. K.

The canonical approach to taking protein crystallography data sets involves

rotating the sample through a range of rotation angles (Δφ), typically on the

order of 0.5 deg. to 2.0 deg., while a single continuous exposure, typically 0.1 s

to 20 s in duration, is taken. During this rotation, multiple diffraction spots will

come into and then leave the plane of the imager, so that the final image contains

an amalgamation of diffraction spots from different rotation angles (φ), though for

the data set to be reconstructible, the angular steps must be small enough so that

individual diffraction spots are distinct and disjoint. The motivation behind this

258

(a) Component Description

(b) Operational Description

Figure 7.11: Annotated protein crystal diffraction stage at the CHESS F2 beam-line. Panel (a) illustrates the main components of this setup while panel (b)illustrates how the crystal is rotated to produce a diffraction series.

259

method is rooted in pragmatism.

To see why this is, one needs to first appreciate that, with the current generation

of x-ray imagers, there is a premium placed on acquiring a diffraction data set in

as few frames as possible. This is due to a combination of a need to minimize

systematic errors in the data set along with a need to acquire the data set as

rapidly as possible. In terms of systematic error, the need to limit the number

of frames results from the long, 1 s or more, dead time required to readout the

imager. To acquire a data set covering a continuous span of rotation angles, this

dead time requires the rotation of the sample be stopped and the sample returned

to a reference point during the imager read out between each rotation step. Even

with the high-precision goniometer used in these experiments, the stopping and

starting of the crystal rotation introduces a small error into the measurement, an

error that is compounded by the number of Δφ steps used to complete the rotation

series. Adding to this uncertainty, the relatively slow, order of 10 ms response

with jitter on the order of ms, x-ray shutters used in these setups contribute an

uncertainty to the rotation angle at which the exposure begins and ends. Thus the

experimenter is faced with the need to cover a sufficient angular span (180 deg.,

90 deg., 45 deg., etc., depending on the symmetries of the crystal) and a trade-off

between angular resolution and absolute angular accuracy in choosing the total

number and size of the angular steps.

A second consideration comes with regards to acquiring the data set as quickly

as possible to preserve the protein crystal quality. Protein crystals are typically

frozen to liquid Nitrogen temperature and then maintained near to this tempera-

ture during data set collection to reduce the rate of radiation damage [35]. Gen-

erally; this damage is taken to be caused by free radicals generated within the

crystal and its preserving liquid, under the influence of radiation. These free rad-

260

icals diffuse through the protein crystal and interact chemically with the protein

molecules, altering the structure of individual crystal elements and thereby degrad-

ing the diffraction pattern. Keeping the crystal cold reduces the rate of damage,

but does not eliminate it, effectively setting a dose limit in which a full data set

must be acquired. This, along with the simple fact that synchrotron beam time is

limited and precious, means that the number of frames needs to be chosen so that

the total time spent reading out the detector is as small a faction as possible of

the total time spent acquiring the data, given the limits imposed by the density of

diffraction spots in the crystals.

The Mixed–Mode PAD offers a solution to the problems, outlined above, with

the canonical approach to data taking. First, thanks to the fast readout capabilities

of this detector, it is possible to acquire a complete data set from a protein crystal

in one un-broken rotation. This is possible because the Mixed–Mode PAD’s front

end acts as an electronic shutter, rejecting signal detected in the detector diode

layer when an exposure is not active.8 This dramatically reduces the time required

to collect a full crystallographic data set while at the same time improving the

quality of the data set by eliminating sources of systematic error. In addition,

this data collection method introduces a, potentially very useful, time correlation

between frames. Synchrotron sources are not always stable, exhibiting potentially

substantial drift due to fluctuations in the beam position and beam intensity. Time

correlation of the image frames provides a good opportunity to characterize and

remove some of this variability through post acquisition filtering.

Finally, the fast framing capabilities of the Mixed–Mode PAD makes it rela-

tively easy to sample the diffraction data set in angular steps that are smaller than

the angular width of the diffraction spots within the set. Known as fine φ-slicing,

8For low-flux circumstances, ≤∼100 10 keV x-rays equiv. per pixel acquired during the deadtime of the detector, or a flux of ∼105 x-rays per second in the final detector, one may actuallyacquire signal during the detector readout, for an effectively dead-time-less device.

261

this technique has seen some limited application in the past (e.g. [45]), but is gen-

erally unaccessible. It is expected, though, that this will change once fast readout

and fast framing Pixel Array Detectors start to become common enough that the

effort required to update aspects of the crystallographic data analysis packages

to make use of this new data becomes worthwhile. However, the advantage of

φ-slicing over the current data collection methods are many.

7.4.3 Synchrotron Measurements

All protein crystallography measurements were made the F2 station at CHESS,

during two runs—one in early April of 2007 and one in mid July of the same year.

In this work, the CHESS F2 beamline scientist, Marian Szebenyi, was extremely

helpful in modifying the crystallography station control software to interface with

the Mixed–Mode PAD. Also, the other members of the Cornell PAD group9 assisted

in setting up and staffing shifts during the run. Buz Barstow, Elizabeth Landrum,

and Chae Un Kim deserve thanks for providing and preparing the crystals used.

During these runs, the vacuum camera housing, discussed in chapter 5, was not

fully operational. As a result, a temporary housing was used in which a flow of

nitrogen gas was used to supply a dry environment in the detector housing. This

allowed limited the temperature at which the Mixed–Mode PAD was operated to

∼8 deg. C. In addition, the camera electronics used with this housing incorporated

a version of the analog readout chain that introduced a substantial amount of noise

(100 to 200 mV, varying between analog output channel) into the measurement of

the analog residual due to a problem decoupling the grounds between the camera

and the remote analog-to-digital converters. Consequently, the noise performance

of the detector in these measurements was substantially less than the sensitivity

9Particularly Mark Tate and Lucas Koerner, but also Hugh Phillips and Marianne Hromalik.

262

which it is capable of.

7.4.3.1 CHESS F2 Beamline

The F2 station is part of the east wing of the CHESS facility and is primar-

ily dedicated to macromolecular crystallography experiments. The station uses

a double-bounce monochromator, two vertically diffracting Si(111) crystals, that

monochromate the synchrotron radiation beam produced by positron bunches as

they pass through the CHESS East 24-pole wiggler. This system is capable of

providing monochromatic beams with a better than 0.1% bandpass over an energy

range from 7.9 keV to 14 keV [20].

7.4.3.2 Full-Sized Detector Mosaic Diffraction Image

The first protein crystallography measurement performed at F2 with the Mixed–

Mode PAD was the acquisition of a full detector sized, ∼512×512 pixel, protein

crystal diffraction pattern. The goal of this measurement was to provide an exam-

ple image to illustrate what could be achieved with a full-size, Mixed–Mode PAD

imager. The crystal used was comprised of the protein Thaumatin, a common and

very robust molecule often used for developing crystallographic methods because

of its well understood structure, ease of crystal growth, and diffraction durability.

For this measurement, sixteen independent images were taken of the same 1 deg.

in 10 s crystal oscillation, between which the Mixed–Mode PAD was translated

relative to the diffraction field. In this way, the image was built up as a series of

mosaic tiles with the resulting diffraction pattern shown in figure 7.10.

7.4.3.3 Spot Comparison

Since the task in an x-ray crystallography diffraction experiment is to measure the

intensity of a set of diffraction spots, it is important to consider how the proper-

263

ties of Mixed–Mode PAD will change this measurement relative to the phosphor-

coupled CCD imagers currently used at most beamlines.

An advantage of the PAD method of directly detecting x-rays over the indirect

detection of phosphor-coupled CCD imagers is the tighter diffraction spots images

that they are able to produce. This is a straightforward consequence of the more

limited spatial response of charge spreading within a diode in comparison to the

spreading of optical light within the phosphor and optical fiber taper of a phosphor-

coupled CCD system. This is illustrated in figure 7.12, which shows the same

diffraction series, from a Thaumatin Protein Crystal, measured with the Mixed–

Mode PAD and the standard commercial phosphor-coupled CCD system10 located

at the beamline.

While the tighter impulse response improves the resolving power of the Mixed–

Mode PAD over phosphor-coupled CCD imagers, and, hence, is expected to im-

prove the crystallographic data set quality, this alone will not fundamentally change

the way in which crystallographic data is taken. There are, however, other capa-

bilities of PAD detectors that have the potential to do this.

7.4.3.4 Continuous Crystal Rotation: φ-Profiling

As mentioned previously, one of the expected advantages of the Mixed–Mode PAD

is to divide a single frame of canonically taken data into a sequence of frames

acquired under continuous rotation of the crystal, providing a detailed picture of

the diffraction spot profile and eliminating excess background. This is illustrated

in figure 7.13, which shows diffraction data from a Thaumatin protein crystal.

Panel (a) of this figure shows the results of a 1 deg., 10 s oscillation taken by

the Mixed–Mode PAD with the canonical, long-exposure, method outlined above.

Panel (b) focuses in on one diffraction spot in this image, detailing the additional

10Quantum-210 (ADSC–Poway, CA).

264

[mm]

[mm

]

-2 0 2

-3

-2

-1

0

1

2

3

(a) Phosphor Coupled CCD

[mm]

[mm

]

-2 0 2

-3

-2

-1

0

1

2

3

(b) Mixed–Mode PAD

ΦΦ

max

[mm]-1 0 1 2

0

0.2

0.4

0.6

0.8

1

(c) 2nd Line, Profile (CCD)

ΦΦ

max

[mm]-1 0 1 2

0

0.2

0.4

0.6

0.8

1

(d) 2nd Line, Profile (PAD)

Figure 7.12: Comparison of identical regions of a Thaumatin diffraction pattern,taken over a 1 deg., 10 s crystal oscillation, with a phosphor-coupled CCD systemand the Mixed–Mode PAD. Panels (a) and (b) display a series of lines of diffractionspots taken with a phosphor-coupled CCD system and the Mixed–Mode PAD(resp.). Panels (c) and (d) show background subtracted contour profiles of thesecond line, indexed from the top of the respective image, normalized to the peakheight of the brightest spot. The point of view for these profiles is taken to bealong the vertical axis of panels (a) and (b) (resp.), in the positive direction. Themissing 4th peak, indexed from the left, in the Mixed–Mode PAD line is due to abad pixel.

265

information that becomes available through fine φ-slicing. In it a one deg., 10 s

crystal oscillation is divided into fifty successive frames taken as the crystal was

continuously rotated for a Δφ resolution of ∼0.02 deg. per frame.11 The integrated

intensity of a single spot is plotted as a function of the crystal oscillation angle.

Dependant on the width of the Δφ resolution, more information may be resolved

from individual diffraction spots.

Profiled Diffraction Spot

(a) Phosphor Coupled CCD

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0.2 0.4 0.6 0.8 1

0

5

10

15

×104

(b) Mixed–Mode PAD

Figure 7.13: Comparison of an element from a canonical macromolecular dataset to the additional information revealed by fine φ-slicing a continuous crystaloscillation. Panel (a) shows a frame taken with the Mixed–Mode PAD containinga 1 deg., 10 s crystal oscillation. In panel (b), the same oscillation is divided into50 frames and the integrated intensity of one diffraction spot, as indicated in panel(a), is profiled.

Beyond the apparent improvement one receives from limiting the integral of the

spot intensity to regions of φ where the spot is actually present, thereby reducing

the background integrated into the spot, increasing the Δφ resolution reveals new

information about the underlying structure of the crystal sample. As figure 7.14

illustrates, as we increase our resolution, we go from blurred measurements of the

11There was a 5 ms delay between frames due to the readout time of the prototype camera.During this time the reset switch of the integrator was used to electronically shutter the detector.

266

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0.2 0.4 0.6 0.8 1

0

5

10

15

×105

(a) Δφ = 0.2 deg.Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0.2 0.4 0.6 0.8 1

0

2

4

6

8

×105

(b) Δφ = 0.1 deg.

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0.2 0.4 0.6 0.8 1

0

1

2

3

4

×105

(c) Δφ = 0.05 deg.

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0.2 0.4 0.6 0.8 1

0

5

10

15

×104

(d) Δφ = 0.02 deg.

Figure 7.14: φ-slicing on the same diffraction spot at differing levels of Δφ reso-lution: 0.2 deg., panel (a); 0.1 deg., panel (b); 0.05 deg., panel (c); and 0.02 deg.,panel (d). This spot was produced by a Thaumatin crystal, with the intensityspread over 15 pixels on the detector, during a 1 deg., 10 s continuous exposure.

267

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]0 0.5 1

0

5

10

15

×104

Figure 7.15: φ-sliced diffraction spot profiles, taken in Δφ = 0.02 deg. steps, for aseries of different spots taken from the same Thaumatin crystal, in the same frameset. The form of the diffraction profile is echoed in each spot, as one expects sincethe profile reflects the underlying structure of the crystal.

total diffracted intensity to being able to resolve the fine profile of this diffraction

spot. In the case of this particular crystal, the information revealed by finely slicing

the Δφ suggests that we have at least two separate crystal domains, evident in the

two peaks in the diffraction profile of the spot.

Another possibility presented by finely slicing the Δφ steps comes from the

repetition of the basic spot profile over all spots within the crystal. As discussed

earlier, the profile of a diffraction spot is determined by the size and mosaic spread

268

of crystallites within the crystal. Hence, it should be the same for every diffraction

spot from a given crystal. This is illustrated in figure 7.15, which shows nine

different diffraction spots from the same crystal, taken in the same 1 deg. in 10

second sequence of frames. This fact can be used to improve the measurement of

the spot intensity and centroid, particularly in weak and noisy spots, by fitting

spot profiles derived from an ensemble of more intense spots.

As a final advantage of this data collection method, it can be used to observe

changes within the crystal induced by external factors. To illustrate this, fine

φ–slicing data sets were taken of a Thaumatin crystal before and after warming

the crystal from 100 deg. K to 170 deg. K. A profile from one diffraction spot

in this data set is shown in figure 7.16. Looking at the normalized overlay, one

sees that warming the crystal, in addition to altering the lattice parameters of the

crystallites as is evident by the shift in the peak position, effects the mosaic spread

of crystallites within the crystal. For example, the sharp shoulder evident in near

an oscillation angle of 2.5 deg. in the 100 deg. K data set has disappeared at 170

deg. K and the full angular spread of the peak has broadened by roughly a third

again upon its original angular spread.

7.4.4 Reflections on Protein Crystallography

The short dead time and high frame rates which the Mixed–Mode PAD is capable

of facilitate new methods of data collection that were previously not possible in

phosphor-coupled CCDs and earlier area x-ray imaging technologies. The acquisi-

tion of data during continuous crystal rotation is one of the most important prac-

tical advances of the Mixed–Mode PAD over the current generation of synchrotron

x-ray imagers. This acquisition mode reduces the total time spent acquiring a

crystallographic data set, removes sources of systematic error, minimizes the back-

269

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]1 2 3 4 5

0

2

4

6

8 ×104

(a) 100 deg. K

Spot

Inte

nsi

ty[A

U]

Oscillation Angle [deg.]1 2 3 4 5

0

2

4

6

8 ×104

(b) 170 deg. K

Oscillation Angle [deg.]

Spot

Inte

nsi

ty[ Φ

(φ)

R dφ

Φ(φ

)

] 100 deg. K

170 deg. K

0 0.5 1 1.5 2

0

0.02

0.04

0.06

0.08

(c) Comparison of Normalized Intensity Profiles

Figure 7.16: Change in the φ-sliced profile of a diffraction spot from a Thaumatincrystal before, panel (a), and after, panel (b), the crystal was warmed from 100deg. K to 170 deg. K at a warming rate of 6 deg. K per minute.

270

ground integrated into each diffraction spot, and gives the experimenter previously

unavailable information by revealing the profile of the diffraction spot.

7.5 Time-Evolving Systems

One area where it is anticipated that Pixel Array Detectors, in particular the

Mixed–Mode PAD, will make significant contributions is in dynamic studies of

time-evolving systems. As mentioned earlier, the current generation of synchrotron

area x-ray imagers require substantial time, typically > 1 s, to read out the de-

tector. Consequently, most time-resolved synchrotron experiments requiring con-

tinuous data acquisition either utilize point or strip detectors [32, 52]. Imaging

experiments are limited to time scales of seconds or longer [90] or utilize tech-

niques like high-speed mechanical or electrical shutter systems to gate x-rays onto

the detector for brief periods of time, building up a temporal mosaic of the system

response [65]. Yet, even with these limitations time-resolved studies of dynamic

systems is a very active field of research.

The Mixed–Mode PAD promises to extend the reach of continuous framing

imaging experiments into the millisecond regime, effectively adding a new dimen-

sion to a domain currently limited to point and strip detectors. It is well suited

to this work, not only because of its fast framing capabilities, but also because of

the large dynamic range it offers for short exposures. To understand this claim

consider that the standard definition of dynamic range,

Dynamic Range =Well Depth

σread

, (7.5)

where σread is the read noise of the detector—canonically taken to be the smallest

signal one can detect above the detector noise12—does not extend well to short

12For a reliably operating photon counting devices this denominator is simply 1, because thisis the smallest level at which one may detect signal.

271

exposures. As an example, consider a photon-counting detector with a well depth

of 220 counts (x-rays) which may be reliably operated up to a flux limit of 106

x-rays/pixel/s. In a 10 ms exposure, this detector can record at most 104 (∼213)

x-rays/pixel, substantially less then the detector total well depth. Consequently,

for short exposures an alternative definition of the detector dynamic range proves

more useful,

Effective Dynamic Range =Φmax · texp

σread

, (7.6)

where Φmax is the per-pixel flux limit of the detector and texp is the exposure

duration. This definition shows the advantage that a detector with a high flux

tolerance, like the 108 x-rays/pixel/s of the Mixed–Mode PAD, has over devices

with lower flux limits in high-speed imaging.

As a first experiment using the Mixed–Mode PAD to study the dynamics of an

evolving system, the imager was employed in the study of homoepitaxial SrTiO3

thin film growth through Pulsed Laser Deposition (PLD). This particular experi-

ment was chosen because it is a system known to exhibit dynamics on millisecond

time scales and is the subject of active research by another group at Cornell.

In the remainder of this section, we first present an overview of the PLD thin-

film growth technique followed by a discussion of the ongoing PLD research being

conducted by our collaborators in this experiment, the Brock Group in the Applied

and Engineering Physics Department at Cornell University. Results form the first

Mixed–Mode PAD PLD experiment are then presented, along with a discussion

of the Mixed–Mode PADs strengths and weaknesses in this experiment. Finally,

we conclude with some comments on the unique possibilities a fast-framing, wide-

effective-dynamic-range, imaging detector offers for time-resolved studies.

272

7.5.1 PLD Overview

Pulsed Laser Deposition (PLD) is a thin film growth technique that has enjoyed

much attention in the research community since the late 1980s when it emerged as

a promising technique for the growth of high–TC superconducting films.13 Today,

it is an active area of research that has expanded significantly from its original

focus on superconducting thin films. Researchers hope to one day be able to grow

materials that would be thermodynamically impossible with other techniques, such

as multilayer films with layers an arbitrary number of monolayers deep or arrays

of quantum dots that could be integrated into optoelectronic or microelectronic

devices [21].

The experimental setup required for PLD thin film growth is relatively straight-

forward. Within a deposition chamber, the beam from a high-powered laser is used

as an external energy source to ablate material from a target. This ablated mate-

rial forms a plume which deposits a thin film of particles on a nearby substrate.

The composition of the target, the ambient environment, the substrate material,

temperature and orientation, as well as the laser pulse duration, intensity, and

wavelength may all be varied to control film growth.

The laser–target and plume–substrate interaction are very complex physical

phenomena. Theoretical descriptions are multidisciplinary combining both equi-

librium and non-equilibrium processes. For this reason, significant amounts of

experimental information are needed to develop accurate descriptions of thin-film

growth. Historically, PLD researchers have relied on post growth microscopy, such

as Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), Scan-

ning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), etc.,

13The history of PLD actually began long before this. The first paper on the topic waspublished in 1965 [91], a few years after the first high-powered ruby lasers became available.However, the field remained somewhat stagnant until the first successful growth of high–TC

superconducting films was reported in 1987.

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to analyze the effects of different growth parameters [21]. This approach suffers

from a number of limitations, foremost being that it is ex-situ, so only information

about the film’s final state is available. Furthermore, in order to be examined,

the substrate must be removed from the deposition environment and cooled, often

hundreds of deg. C, during which changes in the film structure are expected.

In the early part of this decade, work with Reflective High–Energy Electron

Diffraction (RHEED) and x-ray surface studies, the latter made possible by the

availability of two PLD at synchrotron sources (one at the European Synchrotron

Radiation Facility (ESRF) in Grenoble, France and one at CHESS in Ithaca, New

York, USA), yielded in-situ information about film growth that challenged many

assumptions about the processes governing the monolayer growth [21, 32]. The

bulk of the work at millisecond time scales, however, was limited to a general

characterization of film surface roughness, with post growth microscopy relied upon

to characterize surface structures. Very recently, as we will discuss further in

the next section, this work was extended through in-situ measurements in the

scattering plane to reveal information about the correlation length of structures in

the plane of the film, as they evolve during the growth.

7.5.2 PLD Studies by the Brock Group at CHESS

Dr. Joel Brock’s group in the Applied and Engineering Physics Department of

Cornell University has been using the PLD chamber in the CHESS’s G3 hutch to

study thin-film growth using a point detector with the sample in an anti-Bragg

reflection geometry. In this mode, the intensity observed by the detector is directly

related to the surface roughness of the thin film [33]. By depositing less material

than is necessary to complete an atomic layer one can observe oscillations in the re-

flected intensity—typically called RHEED oscillations in deference to their original

274

discovery in electron scattering experiments. This occurs because, under certain

kinetic conditions, deposition of material on a smooth surface serves to roughen

it while deposition on a rough surface serves to smooth it, resulting in periodic

roughening and smoothing of the sample, thereby allowing one to monitor single

molecular layer growth.

While PLD has been shown capable of growing high-quality crystalline films,

a complete model of the PLD process at the atomic level does not exist. The

conventional picture has held that molecules and atoms in the ablation plume strike

the substrate or film surface at randomly distributed positions. These particles may

then evaporate, bond to the surface at existing step edges, or collide with other

particles to nucleate new islands [21]. This treatment assumes that the behavior

of the particles on the surface is predominantly a thermal process, neglecting the

kinetic energy of the incident beam. By using in-situ measurements using the point

detector techniques discussed above, members of Dr. Brock’s group were able to

show, in 2005, that this picture cannot fully explain PLD film growth [32].

More recently, this group has employed a phosphor-coupled CCD operated in

strip detector mode14 in their PLD growth studies. In this operating mode, the

CCD acts as a large 1D detector, accomplished by shifting rows within the CCD

array into the readout register of the CCD, yet waiting to read this register until

it has collected the charge from a full column of exposed pixels. The operation

of shifting charge from pixel rows into the readout register effectively sums the

charge, allowing an entire column of pixels, or sections thereof, to be combined

with very little noise contribution. In addition, the frame rate of the detector is

substantially increased, because the next frame’s worth of data may be acquired

14This mode is sometimes referred to as ‘streak camera mode’; however, this terminology isconfusing as detectors known as streak cameras are often employed in particle accelerators andstorage rings to characterize particle beam properties [88]. As this operation is quite differentfrom how the Brock group has been using their CCD, we adopt the ‘strip detector’ terminologyfor clarity.

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while the current frame is being read from the readout register.

By operating the CCD in strip detector mode, the members of the Brock group

have been able to study the diffuse scattering that accompanies the specular reflec-

tion in the off-axis field on either side of the specular reflection. The profile of this

scattering, as a function of scattering angle, gives information about the length

scales of structures formed as intermediaries of a complete monolayer. Because

the Brock group is, currently, studying the growth of homogeneous monolayers

on a substrate of the same material (homoepitaxial growth) and the system has

only one variable dimension, the size and separation of the monolayer islands, the

scattering only varies in the plane of the sample. Thus, for this experiment, there

is little a 2D detector can offer beyond the capabilities of an ideal 1D detector.

However, the CCD in strip detector mode is far from an ideal 1D detector. A

significant drawback of the strip detector method is that it substantially diminishes

the integrated flux the detector is able to acquire per unit area of each pixel column.

This is because the well depth of the readout register does not change when in

strip mode although the effective area of each pixel increases dramatically. As a

consequence, moderately intense features on the camera in 2D mode may easily

cause it to saturate when operated in strip mode. This is problematic for the PLD

experiment, because it means that it is not possible to measure both the strong

specular reflection and the weak diffuse scattering, in the same image, without

substantial attenuation of the specular intensity.

In contrast, the Mixed–Mode PAD has the ability to measure the entire pattern,

both the specular and diffuse, directly and simultaneously. In addition, its high

frame rate makes imaging the 2D specular and diffuse patterns, on the same time

scales as the Brock Group’s previous 1D measurements, quite straightforward.

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7.5.3 Synchrotron Studies of Monolayer Growth

The PLD measurements were performed at the G3 station at CHESS. The mea-

surements shown here came from one run that lasted for the majority of October

2007.15 This work was done in collaboration with members of Dr. Brock’s group

from the Applied and Engineering Physics Department of Cornell University; in

particular, John Ferguson and Gokhan Arikan, graduate students from this group,

were essential in providing samples, operating the laser and deposition chamber,

as well as assisting in data collection. The G-Line staff scientist, Arthur Woll,

was very helpful by providing example scripts illustrating how we could interface

the Mixed–Mode PAD single hybrid prototype camera to the beamline control

software as well as offering very useful advice on the experiment, as the run pro-

gressed. Members of the Cornell PAD group16 also assisted and much thanks is

especially due to Lucas Koerner for taking on an equal share of the operating time

throughout the duration of the run.

7.5.3.1 CHESS G3 Beamline

The G3 Beamline is a part of the G-line complex built as an addition to the Cor-

nell High Energy Synchrotron Source (CHESS). It operates off of positron bunches

circulating through the 49 pole wiggler that also feeds CHESS West, from the stor-

age ring’s electron current. G3, in particular, is a hutch designed for time–resolved

studies requiring a high flux, delivering upwards of 1013 x-rays/s/mm2. A series of

two synthetic multilayer monochromators are used supply a monochromatic beam

over an energy range of 8 keV to 12 keV with a 1% bandpass [20, 52].

15PLD measurements are extremely time intensive, with pre- and post-sample requiring manyhours. As a result, when everything is working well, testing four or five samples in a 24 hourperiod is an achievement.

16Mark Tate, Marianne Hromalik, and Hugh Philipp assisted in setup and covered some datataking shifts.

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7.5.3.2 Homoepitaxial SrTiO3 Growth

As this data was taken collaboratively with a group that focuses on PLD growth,

and, as such, constitutes a portion of a body of work they are developing, we will

not draw any conclusions regarding PLD growth in this thesis. Instead, we will

focus on the performance of the Mixed–Mode PAD in these experiments. To this

end, we will present data from one homoepitaxial SrTiO3 growth observed with

the Mixed–Mode PAD during this CHESS run. As with most of the other growths,

a series of 800 images were taken,17 where the duration of each exposure was 95

ms with 5 ms spent reading out the imager for a 10 Hz frame rate. The repetition

rate of the laser was set at 0.2 Hz so that 50 frames would be acquired between

each laser shot with the initial firing occurring after the first 50 frames were taken.

The laser used to create the PLD plume was a 348 nm KrF Excimer Laser whose

fluence on the single-crystal SrTiO3 target was ∼2 J-cm2. The separation between

the target and the growth substrate was 6 cm. These substrates were prepared by

members of the Brock group using standard procedures for forming well-ordered

TiO2 terminated (0 0 1) surfaces of SrTiO3 [52]. Typically, an additional annealing

step was performed within an oxygen-rich environment in the growth chamber,

just prior to deposition, to further diminish surface roughness. Details regarding

the growth chamber as well as sample preparation steps may be found in [33].

A typical image captured from a 95 ms integration with the Mixed–Mode PAD

is shown in figure 7.17 where panel (a) shows the detector’s full range while panel

(b) depicts the same image scaled from 0 to ∼10 x-rays. These two panels detail the

two regions of interest, contrasting the intense specular reflection near the center

of the image with its substantially weaker wings of diffuse scattering. The absence

of x-rays outside of ±5 mm of the central axis of the image was due to slitting

17A limitation of the prototype camera that was discussed in chapter 5.

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[mm]

[mm

]

-5 0 5

-5

0

5

(a) Full Scale

[mm]

[mm

]

-5 0 5

-5

0

5

(b) Scaled from 0 to 10, 10 keV X-Rays

Figure 7.17: 95 ms exposure of SrTiO3 at the(0 0 1

4

)after a growth series, shown

if figure 7.18, near maximum diffuse scattering oscillation. Panel (a) is scaled tocover the entire range of the image, from 0 x-rays per pixel to 2,218 x-rays perpixel, while panel (b) is limited to show the diffuse scattering, whose intensity isat most a few x-rays per pixel. Both images are shown in the negative and theintensity floor is set at twice the read noise (2σread) so that spots in the imagesactually represent 1 or more x-rays.

of the beam. Within the un-occulted region, there is interest in the variation

of integrated intensity of the specular reflection and diffuse scattering, as well as

the profile of the diffuse scattering, with time from the start of the growth and

each successive material deposition. Our results for this growth are summarized in

figure 7.18. Panel (a) of this figure depicts the evolution of the integrated specular

intensity with material deposition and surface relaxation. Within the specular

reflection growth oscillations, each maxima represents the completion of a single

SrTiO3 monolayer. Accompanying out of phase oscillations in the integrated diffuse

scattering are shown in panel (b), along with the profile of this scattering in panel

(c).

Before going further, some remarks are warranted to explain how the data

in figure 7.18 was derived from images akin to our example from figure 7.17.

The straightforward method of measuring the specular and diffuse signal with the

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Time from Growth Start [s]

Spec

ula

rIn

tensi

ty[A

U]

0 10 20 30 40 50 60 70

6

8

10

(a) Integrated Reflected Specular Intensity

Time from Growth Start [s]

Diff

use

Inte

nsi

ty[A

U]

0 10 20 30 40 50 60 700.1

0.2

0.3

0.4

(b) Integrated Diffuse Scattering Intensity

Sca

tter

ing

Vec

tor

[A−

1]

Time from Growth Start [s]0 10 20 30 40 50 60 70

0

0.05

0.1

(c) Diffuse Scattering Profile (neg.)

Figure 7.18: Homoepitaxial growth of a SrTiO3 thin film, as observed with theMixed–Mode PAD. Each peak in the reflected specular beam, panel (a), representsthe completion of a single monolayer growth. The accompanying oscillations in thediffuse scattering are shown in integral form in panel (b), while the time evolutionof the diffuse scattering profile are shown in panel (c). This last panel is plottedin the negative with the dark strip at the top of the image denoting the locationand extent of the specular reflection. Dashed vertical lines are included in panels(a) and (b) to denote new material was deposited.

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Mixed–Mode PAD by directly summing the equivalent analog voltage observed in

all pixels at the same scattering vector is problematic for the diffuse scattering,

because it effectively multiplies any coherent noise, in the image by the number

of pixels used in the sum. As the diffuse scattering yield is frequently less than 1

x-ray per pixel per frame, collected over a large area (∼50–100 pixels), even noise

correlations smaller than our digitizer resolution may combine to become signifi-

cant.18 To minimize the systematic error from correlated noise one may restrict

the pixels included in the integration to only those whose measurement contains

signal from one or more x-rays.

Veqv [mV]

[N]

-0.01 0 0.01 0.02 0.030

500

1000

1500

(a) All Pixels

Veqv [mV]

[N]

-0.01 0 0.01 0.02 0.030

50

100

150

200

250

300

(b) Pixels with X-Ray Signal

Figure 7.19: Histogram of the non-specular measurements measurements from asingle image within the SrTiO3 homoepitaxial growth series. Panel (a) shows thecomplete data set along with a fit to the zero x-ray distribution. Panel (b) showsthe remaining data following a cut against pixels with no x-ray signal.

18Part of the reason why the correlated noise is such an issue for this particular measurement,and a global zero correction as was discussed in section 6.2 does not remove the problem, has todo with the structure of the Mixed–Mode PAD analog readout. This device is laid out in eightbanks of sixteen pixels, where the analog residual voltage from eight pixels, one in each bank,are sampled in parallel. Sixteen such samplings reads an entire row of pixels in microseconds,resulting in stronger noise correlations along rows in the imager than columns. Because of thephysical orientation of the Mixed–Mode PAD hybrid in these measurements most pixels in thesame row will contain data at the same scattering vector, thereby introducing systematic noise asa function of scattering angle. In hindsight, this problem could have been avoided by mountingthe detector on its side.

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What makes this ultimately possible is the precision with which the Mixed–

Mode PAD is able to measure the x-ray charge yield, a consequence both of the

quality of the electronics and the high conversion efficiency of direct x-ray detec-

tion. Because of this, a histogram of the signal distribution over the entire image,

an example of which is shown in figure 7.19, reveals the form of the zero x-ray

distribution, i.e. the distribution of measurements from pixels containing no x-ray

signal. Fitting this distribution with a Gaussian, with care to avoid introducing

bias through partial x-ray signal from charge sharing between neighboring pixels,

gives a global offset that can be used to reduce the effect of the noise correction.

In addition, by comparing the amount of signal observed in each bin of the his-

togram with the predictions of this fit, it is possible to assign a probability, for each

pixel, that the measurement it reports contains signal from an x-ray as opposed

to a random noise fluctuation. It is then straightforward to remove the zero x-ray

measurements by comparing, on a pixel by pixel basis, a random number drawn

from a flat distribution to the probability that the measurement from the pixel

contains signal from an x-ray.19 The data remaining after this cut was then used

to determine the scattered intensity as a function of in plane scattering vector.

For the determination of the diffuse scattering profile, the orientation of the

x-ray image as well as the center of the diffraction (q|| = 0) were determined

through a linear fit to the weighted mean of each detector column, i.e. the vertical

element in figure 7.17, pixels within the diffuse scattering region were then binned

based on the minimal separation of their centers and this fitted line. As the

number of elements in each bin could vary, the final parameter reported was the

average intensity observed, calculated by integrating the measurements from all

19This technique could be improved by applying spatial constraints, such as the presence ofan identifiable x-ray signal in a neighboring pixel; however, this is non-trivial to implement and,as the overlap of the x-ray signal and the zero x-ray distribution are sufficiently small and thestatistics sufficiently good, this was generally not deemed necessary.

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Scattering Vector [A−1]

[x-r

ays/

pix

el/s

]

0 0.05 0.12

4

6

8

(a) 1 Frame

Scattering Vector [A−2]

[x-r

ays/

pix

el/s

]

0 0.05 0.12

4

6

8

(b) 5 Frames

Scattering Vector [A−1]

[x-r

ays/

pix

el/s

]

0 0.05 0.12

4

6

8

(c) 10 Frames

Scattering Vector [A−1]

[x-r

ays/

pix

el/s

]

0 0.05 0.12

4

6

8

(d) 20 Frames

Figure 7.20: Diffuse scattering intensity profile near the first specular intensityminima. Panels (a) through (d) show how the profile improves through mergingframes, a combined effect of improved statistics and cancellation of correlated noiseeffects within each frame.

283

pixels determined by the method above to hold x-ray signal and dividing this

result by the total number of pixels within the range of scattering vectors of the

bin. Example results at a portion of the growth are shown in figure 7.20 while

results from the full data set are given in panel (c) of figure 7.18. Merging the data

in this fashion sufficiently reduces the systematic noise to bring out the diffuse

scattering profile, however effects of systematic noise are still evident as it is present

in the pixel measurements with x-ray signal. To mitigate these residual effects of

coherent noise, it is possible to combine data from multiple frames as exemplified

in figure 7.20. Not only does this improve measurement statistics, but coherent

noise fluctuations in the independent images will tend to cancel out, leading to

notable improvement in the the measurement quality.

The scientific implication of the diffuse diffraction profiles, shown individually

in figure 7.20 and as a time series in panel (c) of figure 7.18, is a measurement of the

correlation length of structures on the film surface. A priori, one cannot tell if these

structures represent voids or islands; however, this may be discerned post-growth

through the ex-situ analysis methods mentioned previously. What this information

can directly tell us, though, is if and when intermediate growth structures form on

the surface, their scale and proportional distribution, information that is critical

for the evaluation of theoretical models of PLD thin film growth.

7.5.4 Mixed–Mode PAD Performance Critique

The PLD studies of SrTiO3 homoepitaxial growth reported here demonstrate both

the power and limitations of using the Mixed–Mode PAD for dynamic measure-

ments. As one expects, the Mixed–Mode PAD excelled in measuring the strong,

unattenuated, specular reflection of the synchrotron beam. More difficulty, how-

ever, is found in measuring the diffuse scattering from the growth due to the very

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weak signal levels involved and the need to combine data from a large number

of pixels. Because the Mixed–Mode PAD lacks the pre-sampling summation ca-

pabilities of a CCD, data from each pixel must be sampled independently and

combined offline—a process that makes the system susceptible to even very low

levels, smaller than the quantization threshold of the detector, of correlated noise.

Still, for a 2D detector making a fundamentally 1D measurement the Mixed–Mode

PAD performs quite well.

It is reasonable to ask what would happen if this measurement were performed

with a photon-counting PAD, particularly as such a device would eliminate the

systematic noise seen in the Mixed–Mode PAD. This is, unarguably, quite an

advantage, but it should be noted that it comes at a price in terms of the active

area, as the quantum efficiency of photon-counting PADs is suppressed in the

charge sharing regions between pixels. Given the very weak diffuse background,

this can prove problematic, because correcting for this effectively magnifies the

statistical variations in the signal. Because of this, a more accurate result should

be possible, in cases where a weak flux is combined with a short integration, from

a detector with higher total quantum efficiency. For this to work, though, the

accuracy of the analog measurement must be improved.

As discussed in the conclusion to chapter 4, one way to improve this measure-

ment is to “free-wheel” the analog portion of the Mixed–Mode PAD readout. The

notion behind this is to use the sample and hold circuit in each pixel to sample

the analog data at a much faster than the frame rate. This oversampling offers

improved statistics for the weak analog signal and removes short time scale noise

correlation effects. As our discussion in the conclusion to section 4.4 argues, de-

velopment of this capability is non-trivial, as it requires moderately sophisticated

digital signal processing by the FPGA supporting Mixed–Mode PAD hybrid—yet

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it has the potential to let an analog imager like the Mixed–Mode PAD outperform

a photon-counting PAD in weak-flux dynamic measurements.

7.5.5 Prospects for 2D Growth

The interest in thin film growth is not limited to homogeneous monolayer struc-

tures, though understanding these systems is, arguably, a prerequisite to under-

standing the growth of more complex structures. The devices envisioned as appli-

cations of this technology are multi-layer, potentially with substructure built into

these layers. The continuous dynamics of the growth of such structures cannot

be studied by point or strip detectors because it will require both in-plane and

out-of-plane degrees of freedom. Techniques for these studies have been developed

and active research is currently underway study a variety systems on time scales

longer than 1 s [90].

Detailed description of the Grazing Incidence X-Ray Scattering (GISAXS) tech-

nique can be found in references [84, 89, 60]. Briefly though, GISAXS is a technique

that combines x-ray reflectivity with small angle scattering to provide ensemble

structural information about in-plane and out-of-plane ordering of a thin film. It

has been used extensively to study the growth of block–copolymer systems [36, 90].

Because these systems have evolution time scales on the order of seconds to hours,

dynamical studies can be conducted with the current generation of x-ray detec-

tors. GISAXS has also been used to study PLD films growth [82]. However, these

experiments have not been dynamical studies into the surface science of PLD ma-

terial deposition. Instead, researchers sought to study the evolution of the film as a

function of the number laser pulses, allowing the film to equilibrate after each laser

pulse and before acquiring each GISAXS image. However, as we have discussed,

there are important and poorly understood surface dynamics that occur on short

286

time scales following each laser pulse that equilibrium studies do not address.

Finally, in addition to the possibility of 2D dynamic information that Mixed–

Mode PAD offers, its improved dynamic range and resolving power over the phos-

phor CCDs that have been used in most GISAXS experiments should yield new

information, even on long time scales. As discussed earlier, the images produced

in surface scattering experiments often exhibit strong specular reflection and weak

diffuse scattering signals. These specular reflections are often orders of magnitude

more intense than the diffuse scattering, which becomes a challenge both in terms

of detector dynamic range and Point Spread Function (PSF) that is beyond the

capabilites of most phosphor-coupled CCD systems. Consequently, these CCD sys-

tems rely on beam stops or attenuators to see the weak diffuse signal, a limitation

that is not necessary with the Mixed–Mode PAD.

7.6 Conclusion

The five experiments presented in this chapter serve to illustrate how the capa-

bilities of the Mixed–Mode PAD extend beyond that of the current generation of

x-ray imagers. Combining this detector’s fast framing capabilites and high flux tol-

erance with its single x-ray sensitivity, pixelation limited spatial resolving power,

and substantial dynamic range allows it to acquire data sets that are not possible

with current x-ray imaging technologies. As a result, this detector promises not

only to improve the quality of data sets gathered in currently possible experiments,

but to enable new experiments that were previously impossible.

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CHAPTER 8

CONCLUSIONS

The importance of detector development to the advancement of modern science

was recognized in the press release announcing the 1992 Nobel Prize in Physics,

wherein the Nobel Committee wrote, “The development of detectors very often

goes hand in hand with progress in fundamental research.”1 This observation is at

the heart of the motivation for developing the Mixed–Mode Pixel Array Detector.

Years of investment into synchrotron light sources has yielded sources capable

of producing intense x-ray fluxes, setting the stage for experiments that would

have been impossible with more conventional sources. The full potential for x-

ray science using the very intense x-ray flux from synchrotrons is not, however,

currently being realized because of an absence of suitable detectors. Therefore,

new x-ray detectors that address the limitations of the current generation of x-ray

imagers would enable a broad range of new science.

In the early 1990s, research and development began on a new class of x-ray de-

tectors, Pixel Array Detectors, intended to meet this need. PAD detectors combine

direct x-ray detection with custom, in-pixel signal processing electronics. These

imagers were initially developed along two paths: Digital Pixel Array Detectors,

that use photon discriminating signal processing electronics to count the number

of individual photons observed; and Analog Pixel Array Detectors, that accumu-

late the current generated by the x-ray photons into an analog storage element for

post exposure digitization. Digital PADs offer a large dynamic range and very fast

readout, yet suffer from a dead time associated with processing each photon that,

effectively, imposes a flux limits on these detectors that is low in comparison to the

x-ray intensities attainable in many synchrotron experiments. On the other hand,

1In 1992 the Nobel Prize in Physics was awarded to Professor Georges Charpak for his inven-tion and development of particle detectors, in particular the multi-wire proportional chamber.

289

Analog PADs can tolerate the extremely intense x-ray fluxes produced at modern

synchrotron light sources but are limited in terms of their dynamic range and, in

designs that do not incorporate a high level of parallel digitization and read out,

frame rate. The Mixed–Mode PAD merges the integrating front end of an Analog

PAD with the digital storage of a Digital PAD to achieve a device that is more

than the sum of its components.

In this final chapter, we will briefly review the characteristics that distinguish

the Mixed–Mode PAD, both from the current generation of x-ray imagers employed

at synchrotron light sources and from other contemporary PAD projects, and the

opportunities these characteristics present for science at synchrotron light sources.

8.0.1 Performance Highlights

What enables the Mixed–Mode PAD to extend science at synchrotron light sources

is a combination of performance characteristics that is unique to this imager and

well suited to brightness of the modern synchrotron. Within the melange of imager

properties discussed over the course of this thesis, two classes of distinguishing

characteristics can be identified: those that distinguish the PAD methodology

from current generations of non-PAD x-ray detectors, and therefore are held in

common with all PADs; and those that distinguish the Mixed–Mode PAD from its

Analog and Digital PAD contemporaries.

The characteristics of the Mixed–Mode PAD that distinguish it from the cur-

rent generation of synchrotron imagers, but that it holds in common with all

PAD detectors, are benefits it receives from direct x-ray detection. These bene-

fits include a comparatively large signal yielded per x-ray with intrinsically small

variation (e.g. for a 10 keV x-ray one expects 445 ± 3 aC of charge yield from a

PAD as opposed to 2 to 5 ± 2 to 3 aC for a phosphor coupled CCD) that allows

the Mixed–Mode PAD to observe quanta of x-rays (as was demonstrated in section

290

7.1) and Digital PADs to reliably count single x-rays. In addition, direct detection

results in an analog impulse response that is constrained to a small spatial region,

typically less than the size of a PAD pixel, thus making it possible to resolve very

faint x-ray signals in close proximity to intense x-ray signals. Finally, though not

a prerequisite, the signal processing electronics of the Mixed–Mode PAD and all

contemporary PADs offer an electronic shutter that controls the gating of x-ray

signal into the PAD signal processing chain; this, in-turn, frees PAD detectors from

the experimental limitations and timing uncertainty introduced by the mechanical

shutters required by the current generation of synchrotron imagers.

The characteristics that distinguish the Mixed–Mode PAD from other PADs

stem from the signal processing electronics built into each pixel. Foremost among

these characteristics are the large well depth (2.6 × 107 x-rays/pixel2) and single

x-ray sensitivity (through a FWHM read noise of 0.4 x-ray) that give the Mixed

Mode PAD a dynamic range of 156 dB; in comparison with 120 dB for the largest

dynamic range Digital PAD or 76 dB for the largest dynamic range Analog PAD.

Similarly important, particularly for imaging with brief exposures, is the 108 x-

rays/pixel/s flux tolerance of the Mixed–Mode PAD, two orders of magnitude

higher than what can be expected from a contemporary Digital PAD. This high

flux tolerance makes more of the imager dynamic range available in brief exposures,

as per the discussion of section 7.5. Finally, the capacity of the Mixed–Mode PAD

detector hybrids to accurately readout in < 1 ms offers continuous frame rates

up to 1 kHz, which is roughly equal to the continuous frame rates that may be

obtained from Digital PADs but much faster than all but the most highly parallel

of Analog PADs.

2All x-ray referenced parameters in this chapter assume an x-ray energy of 10 keV.

291

8.0.2 Science Opportunities

While the individual performance characteristics noted above all represent signifi-

cant advancements beyond the capabilities of the current generation of synchrotron

imagers, what ultimately distinguishes the Mixed–Mode PAD from contemporary

PAD projects is the combination of these characteristics that it offers. This com-

bination places the Mixed–Mode PAD in a unique position to effectively make use

of the intense x-ray fluxes available at modern synchrotron light sources to extend

x-ray science to new areas.

One very important property that the Mixed–Mode PAD brings to x-ray scat-

tering experiments is its combination of large dynamic range and sub-pixel point

spread. In earlier imagers, like phosphor-coupled CCDs, indirect x-ray detection

would yield non-negligible signal on mm length scales. This effectively imposes a

dynamic range limit on these imagers by making it very difficult to resolve weak

signals in the presence of the presence of strong ones. In a direct detection imager,

like the Mixed–Mode PAD, the analog response of the detector diode to each x-ray

is concentrated to within a sufficiently small spatial region that, so long as there

is a pixel separating the weak and intense signals, it is possible to resolve them

both. However, to measure both signals requires, in addition to resolving power,

sufficient dynamic range to observe both with good statistics. As scattering sys-

tems can produce peaks or rings of scattered intensity that differ by many orders of

magnitude and synchrotron sources provide sufficient flux to observe these on rea-

sonable time scales, the availability of a detector that offers the dynamic range of

the Mixed–Mode PAD with the resolving power of direct detection will reveal new

information in currently studied systems while enabling the investigation of new

systems are beyond the resolution and dynamic range limits of current detectors.

The potential the Mixed–Mode PAD offers for studying wide-dynamic-range

292

systems is, however, not limited to static measurements. One of the most excit-

ing application area for the Mixed–Mode PAD is in the imaging of systems that

are continuously evolving on ms time scales. Currently, this time scale is almost

exclusively the domain of point or 1D detectors, as imagers capable of framing on

this time scale are simply not available.

The Digital PADs, currently in development, offer electronic shuttering capa-

bilities and small read out dead time required to frame at the high rate needed for

work on ms time scales; however, because of their flux limitations they are limited

in the effective dynamic range that they offer for short exposures. The Mixed–

Mode PAD also possess electronic shuttering capabilities and small read out dead

time but combines these performance characteristics with a flux tolerance two or-

ders of magnitude higher than what one can expect from a well calibrated Digital

PAD. Consequently, it is a device that is uniquely well suited to imaging on ms

time scales and, therefore, is poised to enable investigation of previously inacces-

sible dynamic systems with x-rays.

8.0.3 Work Ahead

The work presented in this thesis demonstrated the functionality and capabilities

of the Mixed–Mode PAD while illustrating it potential impact on science at syn-

chrotron light sources through a series of demonstration experiments. This work

was performed using a single hybrid prototype camera, as was discussed in chap-

ter 5. While this prototype served as a good characterization and demonstration

platform, its practical utility is limited by its small active area.

However, as was also discussed in chapter 5, while this characterization work

and the inaugural synchrotron experiments using the Mixed–Mode PAD were un-

dertaken at Cornell, our industrial collaborators at ADSC have been working to-

293

wards developing custom support electronics and a cryostat housing suitable for

a large-area (512 × 512 pixel/4 × 4 detector hybrid) camera. As this phase of

the project is, fundamentally, a commercialization effort, the involvement of the

Cornell Detector Development Group is limited to an advisory role.

Tangentially, an effort is underway by the Cornell Detector Development Group

to upgrade the support electronics of the single hybrid prototype camera to support

four detector hybrids in a 1×4 configuration (128×512 pixel). This imager would

have limited utility for application requiring large 2D area coverage, such as the

crystallography market that our collaborators at ADSC are targeting. However, it

should be very useful when employed at the G-line facility of CHESS, where there

is much interest in studying the dynamics of thin film growth processes as well

as solution scattering in the small angle regime—systems that require substantial

active area in one dimension but much less in the other.

8.0.4 Closing Remarks

It was argued in the introduction to this thesis that, for the development of new in-

strumentation to be of scientific merit, it should be designed with, and demonstrate

an ability to, enable a broad class of new scientific investigation. The Mixed–Mode

PAD demonstrably meets these objectives by bridging a portion of the gulf between

the capacity of synchrotron light sources to produce intense x-ray fluxes and the

capabilities of modern x-ray detectors to measure the resulting signals. In the pro-

cess, it offers the first opportunities for wide dynamic range, continuous imaging

of dynamic phenomena on ms times scales using x-rays.

294

APPENDIX A

LINEAR FEEDBACK SHIFT REGISTER THEORY

The theory underlying the operation of the pseudorandom counter is the theory

of finite fields, which was originally built on a foundation created by the French

mathematician Evariste Galois.1 The circuit itself springs from considerations of

the reducibility of polynomials over finite fields; in particular, the binary field

Z/2Z = {0, 1}. As this is a topic that has been worthy of many texts, we will only

present an overview oriented discussion, sketching out the details as they relate

to our particular application. Readers interested in a deeper explanation of finite

fields are referenced to [24] as well as [37] for further details on their application

to the theory of Linear Feedback Shift Registers (LFSR).

a1 a2 a3out

a4

Figure A.1: Example linear feedback shift register.

To illustrate the problem, we begin by looking at an example of an LFSR that

would be unsuitable for a counter, because it cannot reach all possible register

states and analyzing the properties that indicate this. Consider the three-tap

Fibonacci mode LFSR shown in figure A.1. We may write the state of this register

1Evariste Galois, 1811-1832. Quite a unique figure in the history of mathematics. While stillin his teens, he determined a necessary and sufficient condition for a polynomial to be solvableby radicals, laying the foundation for the branch of Finite Field Theory known as Galois Theory.He died from wounds suffered in a duel at the age of twenty; whether the cause of the duel waspolitics or a matter of the heart is a point of debate.

295

as a vector

a =

⎛⎜⎜⎜⎜⎜⎜⎜⎝

a1

a2

a3

a4

⎞⎟⎟⎟⎟⎟⎟⎟⎠, (A.1)

where each component (a1, a2, a3, and a4) is a member of the binary field (Z/2Z)).

Given a state vector a, to generate the register’s next state we apply the generation

operator (G),

G =

⎛⎜⎜⎜⎜⎜⎜⎜⎝

0 1 0 0

0 0 1 0

0 0 0 1

1 0 1 1

⎞⎟⎟⎟⎟⎟⎟⎟⎠, (A.2)

or more generally if a0 is the initial state of the system then the kth subsequent

state is given by ak = Gk · a0. Since we are working with a nonsingular generator

on a finite vector space, for every state there exists an integer p such that Gpa = a

or equivalently Gp = I, where I is the identity matrix. The integer p is said to

be the period of the generation operator for that vector and the period is termed

maximal if p = bd − 1, where b base of the finite field comprising the vector space

components (2 in the case of the binary field) and d is the dimensionality of the

space. Inspection shows that this is one less than the total number of possible

states and the largest period achievable, as the null vector will always generate a

separate, singular subspace. The splitting of this vector space by the generator

defined above is shown in figure A.2. As this figure illustrates, this generator splits

the 16 possible states into four subspaces and as such does not yield a maximal

period.

296

1000

0001

0011

01101101

1010

0100

0000

1111

0111

1110

1100

10010010

0101

1011

Figure A.2: Graphical descriptions how the generator Ω, as defined in equationA.2, splits vector space of 4-tuples with binary components, (Z/2Z) ⊗ (Z/2Z) ⊗(Z/2Z)⊗ (Z/2Z).

A more direct, though much less illustrative, path to this result comes from

considering the characteristic polynomial of the generation operator, G,

g(x) = det (x · I − G) (A.3)

= x4 − x3 − x2 − 1

= x4 + x3 + x2 + 1

= (x+ 1)(x3 + x+ 1), (A.4)

where we have used the fact that for x ∈ Z/2Z, x = −x to arrive at our final

simplification. As in traditional linear algebra, the characteristic polynomial of

the generator can reveal much about its behavior. For our purposes, of principle

importance is the polynomial’s reducibility ; that is, whether the polynomial may

be written as the product of two or more distinct polynomials without remainder.

If the characteristic polynomial can be reduced, then the vector space will split

under the generator’s operation, as our example illustrated, and thus the generator

cannot be maximal. If, however, the characteristic polynomial (g(x)) is irreducible

then Finite Fields Theory assures us that it will divide f(x) = xbD(g)−1 − 1, where

b is again the base of our finite field (2 in this case) and D(g) is the degree of the

characteristic polynomial. Now, if g divides f , then any root of g is also a root

297

of f and since the operator G is a root of its characteristic polynomial, g, G must

also be a root of f . This is equivalent to saying

GbD(g)−1 = I. (A.5)

Unfortunately, we are not guaranteed that bD(g)−1 is the smallest integer exponent

for which G raised to that power becomes the identity, only that the smallest

integer exponent will divide bD(g)− 1. Polynomials which are both irreducible and

maximal are termed primitive. To verify if a particular operator is primitive what

remains is to check if g divides xk − 1 for any integer k that divides bD(g) − 1.

While computationally laborious if done by hand algorithms exist to allow this

to be efficiently checked by computer. In this way, analysis of the characteristic

polynomial provides a direct and efficient method for determining if a generator

has a maximal period.

Although this operator approach offers a pedagogically straightforward means

to determine if a LFSR is maximal, most treatments of the Fibonacci mode LFSR

architecture do not invoke it as there is a much simpler way of deriving the systems

characteristic polynomial. More frequently referred to in the literature as the

connection polynomial, it is defined as

q(x) =m∑

i=0

qix(m−i), (A.6)

where m is the number of bits in the register, qi = 1 if there is a tap on the ith

bit (using the indexing from figures 4.20 and A.1) or 0 otherwise, and q0 = 1 by

definition. The connection polynomial is equivalent to the generator operator’s

characteristic polynomial, and, thus, it may be analyzed analogously to determine

if a LFSR has a maximal period.

298

APPENDIX B

FREQUENCY ANALYSIS OF INTEGRATOR WITH INJECTED

CURRENT

Cint

A(t)

−

+Vref

Z

VA

VB

δI

Figure B.1: Model used in current injection analysis.

From figure B.1, the impedance seen looking into node VA is given by(Z∣∣∣∣∣∣ 1

iωCint(1 + A)

)=

Z

1 + iωCintZ(1 + A), (B.1)

where A is the amplifier gain at the frequency ω. Then, if a current (δI) is injected

into this node at the frequency ω,

δVA =Z

1 + iωCintZ(1 + A)· δI, (B.2)

and

δVB = −AδVA (B.3)

= − ZA

1 + iωCintZ(1 + A)· δI. (B.4)

For the special case of Z = 1iωCpix

, this result simplifies to

δVB = − A

iω(Cpix + Cint(1 +A))· δI. (B.5)

299

APPENDIX C

ASIC SUBMISSION HISTORY

All submissions were fabricated using the TSMC 0.25 μm process, contracted

through the Metal Oxide Semiconductor Implementation Service (MOSIS) service.

Each submission is accompanied by release documentation, prepared by Skip Au-

gustine, containing full schematics a list of design changes. This documentation is

on record with the Cornell X-Ray Detector Development Group.

Table C.1: Mixed–Mode PAD prototyping submission history.

Submission ID Date Comment

Cornell.A Nov. 2003 Test structuresAE176 Jan. 2004 16× 128 pixel arrayAE180 Mar. 2004 16× 16 pixel arrayCornell.B May 2004 Test structuresAE184 Aug. 2004 16× 16 pixel arrayAE190 Apr. 2005 16× 128 pixel arrayAE196 Aug. 2005 16× 16 pixel arrayAE203 Nov. 2005 16× 16 pixel arrayAE207 Feb. 2006 Final 128× 128 pixel array

301

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